{"segment":[{"time":24,"part":[{"title":"Ch\u1ecdn <u>nh\u1eefng<\/u> \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"Ch\u1ecdn \u0111\u01b0\u1ee3c nhi\u1ec1u \u0111\u00e1p \u00e1n","temp":"checkbox","correct":[["1","3","5"]],"list":[{"point":5,"img":"","ques":" Trong c\u00e1c bi\u1ec3u th\u1ee9c sau, nh\u1eefng bi\u1ec3u th\u1ee9c n\u00e0o v\u1eeba l\u00e0 <b> \u0111\u01a1n th\u1ee9c<\/b> v\u1eeba l\u00e0 <b> \u0111a th\u1ee9c<\/b>? ","hint":"","column":3,"number_true":3,"select":["A. $x^{2018}$","B. $20+xy$","C. $-22$","D. $1+x+x^2$","E. $\\dfrac{x}{2}$","F. $\\dfrac{1}{4}(y+1)$"],"explain":"<span class='basic_left'> Ta bi\u1ebft r\u1eb1ng: M\u1ed7i \u0111\u01a1n th\u1ee9c c\u0169ng \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 m\u1ed9t \u0111a th\u1ee9c. <br\/> Do \u0111\u00f3, trong c\u00e1c bi\u1ec3u th\u1ee9c \u0111\u00e3 cho, nh\u1eefng bi\u1ec3u th\u1ee9c sau v\u1eeba l\u00e0 <b> \u0111\u01a1n th\u1ee9c<\/b> v\u1eeba l\u00e0 <b> \u0111a th\u1ee9c<\/b>: <br\/> A. $x^{2018}$ <br\/> C. $-22$ <br\/> E. $\\dfrac{x}{2}$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n ch\u1ecdn l\u00e0 A, C v\u00e0 E.<\/span><\/span>"}]}],"id_ques":1271},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> K\u1ebft qu\u1ea3 thu g\u1ecdn c\u1ee7a \u0111\u01a1n th\u1ee9c $3ak^2(-2kx^3)k^3x$ l\u00e0: <\/span>","select":["A. $-6ak^6x^4$","B. $6ak^6x^4$","C. $-6ak^6x^3$","D. $6ak^5x^3$"],"hint":"","explain":"<span class='basic_left'> Ta c\u00f3: <br\/> $3ak^2(-2kx^3)k^3x= [3.(-2)]a(k^2kk^3)(x^3x)=-6ak^6x^4$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span><\/span>","column":2}]}],"id_ques":1272},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["11"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" B\u1eadc c\u1ee7a \u0111a th\u1ee9c $12x^6yz^4+24x^4yz-55$ l\u00e0 _input_ ","hint":"B\u1eadc c\u1ee7a \u0111a th\u1ee9c l\u1ea5y theo b\u1eadc c\u1ee7a h\u1ea1ng t\u1eed c\u00f3 b\u1eadc cao nh\u1ea5t trong \u0111a th\u1ee9c \u0111\u00f3.","explain":"<span class='basic_left'> \u0110a th\u1ee9c $12x^6yz^4+24x^4yz-55$ g\u1ed3m c\u00f3 ba h\u1ea1ng t\u1eed, trong \u0111\u00f3 h\u1ea1ng t\u1eed $12x^6yz^4$ c\u00f3 b\u1eadc cao nh\u1ea5t l\u00e0 $11$ <br\/> Do \u0111\u00f3, b\u1eadc c\u1ee7a \u0111a th\u1ee9c \u0111\u00e3 cho l\u00e0 $11$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $11$.<\/span><\/span>"}]}],"id_ques":1273},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["10"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'>Cho \u0111\u01a1n th\u1ee9c $-2x^2y^3z.(-4xz^3)$ <br\/> B\u1eadc c\u1ee7a \u0111\u01a1n th\u1ee9c sau khi thu g\u1ecdn l\u00e0 _input_ <\/span> ","hint":"Mu\u1ed1n nh\u00e2n hai \u0111\u01a1n th\u1ee9c ta nh\u00e2n h\u1ec7 s\u1ed1 v\u1edbi h\u1ec7 s\u1ed1, bi\u1ebfn v\u1edbi bi\u1ebfn.","explain":"<span class='basic_left'> Ta c\u00f3: <br\/> $-2x^2y^3z.(-4xz^3)=(-2).(-4)(x^2x)y^3(zz^3)=8x^3y^3z^4$ <br\/> B\u1eadc c\u1ee7a \u0111\u01a1n th\u1ee9c sau khi thu g\u1ecdn l\u00e0 $10$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $10$.<\/span><\/span>"}]}],"id_ques":1274},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["24"],["5"],["1"],["12"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> Cho b\u1ea3ng sau v\u00e0 \u0111i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o c\u00e1c \u00f4 tr\u1ed1ng: <br\/> <table><tr><th>\u0110\u01a1n th\u1ee9c<\/th><th>H\u1ec7 s\u1ed1 c\u1ee7a \u0111\u01a1n th\u1ee9c<\/th><th>B\u1eadc c\u1ee7a \u0111\u01a1n th\u1ee9c<\/th><\/tr><tr><td>$2^3xyz.(3xy)$<\/td><td>_input_<\/td><td>_input_<\/td><\/tr><tr><td>$4{{x}^{2}}{{y}^{2}}.{{\\left( -\\dfrac{1}{2}x{{y}^{2}}z \\right)}^{2}}$<\/td><td>_input_<\/td><td>_input_<\/td><\/tr><\/table> <\/span> ","hint":"Mu\u1ed1n nh\u00e2n hai \u0111\u01a1n th\u1ee9c ta nh\u00e2n h\u1ec7 s\u1ed1 v\u1edbi h\u1ec7 s\u1ed1, bi\u1ebfn v\u1edbi bi\u1ebfn.","explain":"<span class='basic_left'> Ta c\u00f3: <br\/> $2^3xyz.(3xy)=8xyz.3xy=24x^2y^2z$ <br\/> $\\Rightarrow$ \u0110\u01a1n th\u1ee9c c\u00f3 h\u1ec7 s\u1ed1 $24$ v\u00e0 b\u1eadc l\u00e0 $5$ <br\/> $4{{x}^{2}}{{y}^{2}}.{{\\left( -\\dfrac{1}{2}x{{y}^{2}}z \\right)}^{2}}=4{{x}^{2}}{{y}^{2}}.\\dfrac{1}{4}{{x}^{2}}{{y}^{4}}{{z}^{2}}={{x}^{4}}{{y}^{6}}{{z}^{2}}$ <br\/> $\\Rightarrow$ \u0110\u01a1n th\u1ee9c c\u00f3 h\u1ec7 s\u1ed1 l\u00e0 $1$ v\u00e0 b\u1eadc l\u00e0 $12$ <br\/> Do \u0111\u00f3, ta c\u00f3 b\u1ea3ng ho\u00e0n ch\u1ec9nh nh\u01b0 sau: <br\/> <table><tr><th>\u0110\u01a1n th\u1ee9c<\/th><th>H\u1ec7 s\u1ed1 c\u1ee7a \u0111\u01a1n th\u1ee9c<\/th><th>B\u1eadc c\u1ee7a \u0111\u01a1n th\u1ee9c<\/th><\/tr><tr><td>$2^3xyz.(3xy)$<\/td><td>$24$<\/td><td>$5$<\/td><\/tr><tr><td>$4{{x}^{2}}{{y}^{2}}.{{\\left( -\\dfrac{1}{2}x{{y}^{2}}z \\right)}^{2}}$<\/td><td>$1$<\/td><td>$12$<\/td><\/tr><\/table> <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $24;5;1;12$<\/span><\/span>"}]}],"id_ques":1275},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Thu g\u1ecdn bi\u1ec3u th\u1ee9c $-x^7y-2x^7y+9x^7y-5x^7y$ \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 l\u00e0: <\/span>","select":["A. $x^7y$","B. $9x^7y$","C. $3x^7y$","D. $-x^7y$"],"hint":"Th\u1ef1c hi\u1ec7n c\u1ed9ng (tr\u1eeb) c\u00e1c \u0111\u01a1n th\u1ee9c \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Bi\u1ec3u th\u1ee9c \u0111\u00e3 cho c\u00f3 c\u00e1c h\u1ea1ng t\u1eed l\u00e0 c\u00e1c \u0111\u01a1n th\u1ee9c \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau. <br\/> Mu\u1ed1n c\u1ed9ng (tr\u1eeb) c\u00e1c \u0111\u01a1n th\u1ee9c \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau ta c\u1ed9ng (tr\u1eeb) c\u00e1c h\u1ec7 s\u1ed1 v\u1edbi nhau v\u00e0 gi\u1eef nguy\u00ean ph\u1ea7n bi\u1ebfn. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $-x^7y-2x^7y+9x^7y-5x^7y=(-1-2+9-5)x^7y=x^7y$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span><\/span>","column":2}]}],"id_ques":1276},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho \u0111a th\u1ee9c $B=8{{x}^{3}}y-2x{{y}^{2}}+10{{x}^{3}}{{y}^{3}}+3x{{y}^{2}}-4{{x}^{3}}y-10{{x}^{3}}{{y}^{3}}$ <br\/> \u0110a th\u1ee9c n\u00e0o sau \u0111\u00e2y l\u00e0 \u0111a th\u1ee9c thu g\u1ecdn c\u1ee7a $B$: <\/span>","select":["A. $xy^2-3x^3y $","B. $x^2y-xy^2+8x^3y^3$","C. $4x^3y+xy^2$","D. M\u1ed9t k\u1ebft qu\u1ea3 kh\u00e1c"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Nh\u00f3m c\u00e1c \u0111\u01a1n th\u1ee9c \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau r\u1ed3i thu g\u1ecdn.<br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $\\begin{align} & B=8{{x}^{3}}y-2x{{y}^{2}}+10{{x}^{3}}{{y}^{3}}+3x{{y}^{2}}-4{{x}^{3}}y-10{{x}^{3}}{{y}^{3}} \\\\ & \\,\\,\\,\\,\\,\\,=\\left( 8{{x}^{3}}y-4{{x}^{3}}y \\right)+\\left( -2x{{y}^{2}}+3x{{y}^{2}} \\right)+\\left( 10{{x}^{3}}{{y}^{3}}-10{{x}^{3}}{{y}^{3}} \\right) \\\\ & \\,\\,\\,\\,\\,\\,=4{{x}^{3}}y+x{{y}^{2}} \\\\ \\end{align}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span><\/span>","column":2}]}],"id_ques":1277},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-765"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> Gi\u00e1 tr\u1ecb c\u1ee7a \u0111a th\u1ee9c $x^3-2x+5x^3-2x^2-5x$ t\u1ea1i $x=-5$ l\u00e0 _input_ <\/span> ","hint":"","explain":"<span class='basic_left'> Ta c\u00f3: <br\/> $x^3-2x+5x^3-2x^2-5x$<br\/> $=(x^3+5x^3)-2x^2+(-2x-5x)$ <br\/> $=6x^3-2x^2-7x$ <br\/> Thay $x=-5$ v\u00e0o k\u1ebft qu\u1ea3 tr\u00ean, ta \u0111\u01b0\u1ee3c: <br\/> $6.(-5)^3-2.(-5)^2-7.(-5)=-765$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-765$<\/span><\/span>"}]}],"id_ques":1278},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":" <span class='basic_left'> T\u00ecm \u0111a th\u1ee9c $A,$ bi\u1ebft: <br\/> $A-\\left( {{x}^{2}}y-2x{{y}^{2}}+xy+1 \\right)={{x}^{2}}y+x{{y}^{2}}-xy-1$ <\/span>","select":["A. $A=-x{{y}^{2}}+2xy-2$","B. $A=2{{x}^{2}}y+x{{y}^{2}}-2xy$","C. $A=2{{x}^{2}}y-x{{y}^{2}}+2xy$","D. $A=2{{x}^{2}}y-x{{y}^{2}}$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Mu\u1ed1n t\u00ecm \u0111a th\u1ee9c b\u1ecb tr\u1eeb ta l\u1ea5y \u0111a th\u1ee9c hi\u1ec7u c\u1ed9ng v\u1edbi \u0111a th\u1ee9c tr\u1eeb. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $\\begin{align} & A-\\left( {{x}^{2}}y-2x{{y}^{2}}+xy+1 \\right)={{x}^{2}}y+x{{y}^{2}}-xy-1 \\\\ & \\Rightarrow A=\\left( {{x}^{2}}y+x{{y}^{2}}-xy-1 \\right)+\\left( {{x}^{2}}y-2x{{y}^{2}}+xy+1 \\right) \\\\ & \\,\\,\\,\\,\\,\\,={{x}^{2}}y+x{{y}^{2}}-xy-1+{{x}^{2}}y-2x{{y}^{2}}+xy+1 \\\\ & \\,\\,\\,\\,\\,\\,=\\left( {{x}^{2}}y+{{x}^{2}}y \\right)+\\left( x{{y}^{2}}-2x{{y}^{2}} \\right)+\\left( -xy+xy \\right)+\\left( -1+1 \\right) \\\\ & \\,\\,\\,\\,\\,\\,=2{{x}^{2}}y-x{{y}^{2}} \\\\ \\end{align}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span><\/span>","column":2}]}],"id_ques":1279},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" <span class='basic_left'> C\u00e1c nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c $B(x)=x^3+25x$ l\u00e0: <\/span>","select":["A. $x=-5;x=5$","B. $x=0$","C. $x=-5;x=0;x=5$","D. $x=-25$"],"hint":"","explain":"<span class='basic_left'> Ta c\u00f3: <br\/> $B(x)=0$ <br\/> $\\Rightarrow x^3+25x=0$ <br\/> $\\Rightarrow x(x^2+25)=0$ <br\/> $\\Rightarrow x=0$ (do $x^2+25 \\ge 25 > 0$ v\u1edbi m\u1ecdi $x$) <br\/> Do \u0111\u00f3, \u0111a th\u1ee9c $B(x)=x^3+25x$ ch\u1ec9 c\u00f3 m\u1ed9t nghi\u1ec7m l\u00e0 $x=0$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span><\/span>","column":2}]}],"id_ques":1280},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":" <span class='basic_left'> T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean $n$ bi\u1ebft: $(3x^3y^2)(2x^ny)=6x^7y^3$ <\/span>","select":["A. $n=2$","B. $n=3$","C. $n=4$","D. $n=5$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>Thu g\u1ecdn v\u1ebf tr\u00e1i sau \u0111\u00f3 \u0111\u1ed3ng nh\u1ea5t hai v\u1ebf \u0111\u1ec3 t\u00ecm $n$ <br\/> \u00c1p d\u1ee5ng: $a^n=a^m \\Rightarrow m=n$ v\u1edbi $a \\ne 0;1$<br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $(3x^3y^2)(2x^ny)=6x^7y^3$ <br\/> $\\Rightarrow (3.2)(x^3x^n)(y^2y)=6x^7y^3$ <br\/> $\\Rightarrow 6x^{3+n}y^3=6x^7y^3$ <br\/> $\\Rightarrow 3+n=7$ <br\/> $\\Rightarrow n=4$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span><\/span>","column":2}]}],"id_ques":1281},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0111\u00e2y \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" Hai \u0111\u01a1n th\u1ee9c $5x^3y$ v\u00e0 $-3xy^5$ c\u00f3 c\u00f9ng gi\u00e1 tr\u1ecb d\u01b0\u01a1ng v\u1edbi m\u1ecdi $x,y.$","select":["\u0110\u00fang","Sai"],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>T\u00ednh t\u00edch c\u1ee7a hai \u0111\u01a1n th\u1ee9c \u0111\u00e3 cho v\u00e0 nh\u1eadn \u0111\u1ecbnh gi\u00e1 tr\u1ecb c\u1ee7a t\u00edch \u0111\u00f3. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta x\u00e9t t\u00edch hai \u0111\u01a1n th\u1ee9c \u0111\u00e3 cho: <br\/> $5x^3y.(-3xy^5)=[5.(-3)](x^3x)(yy^5)=-15x^4y^6$ <br\/> Ta th\u1ea5y: $x^4 \\ge 0; y^6 \\ge 0$ v\u1edbi m\u1ecdi $x,y$ <br\/> $\\Rightarrow -15x^4y^6 \\le 0$ v\u1edbi m\u1ecdi $x,y$ <br\/> Do \u0111\u00f3, kh\u1eb3ng \u0111\u1ecbnh tr\u00ean \u0111\u1ec1 b\u00e0i l\u00e0 sai. <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 Sai.<\/span> <\/span>","column":2}]}],"id_ques":1282},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0111\u00e2y \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'>Cho ba \u0111\u01a1n th\u1ee9c: $\\dfrac{3}{5}x^2y^3; -2x^4y^2$ v\u00e0 $-\\dfrac{1}{6}x^2y^5$ <br\/> Ba \u0111\u01a1n th\u1ee9c tr\u00ean kh\u00f4ng th\u1ec3 c\u00f9ng c\u00f3 gi\u00e1 tr\u1ecb \u00e2m v\u1edbi m\u1ecdi $x,y.$ <\/span> ","select":["\u0110\u00fang","Sai"],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>T\u00ednh t\u00edch c\u1ee7a ba \u0111\u01a1n th\u1ee9c \u0111\u00e3 cho v\u00e0 nh\u1eadn \u0111\u1ecbnh gi\u00e1 tr\u1ecb c\u1ee7a t\u00edch \u0111\u00f3. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta x\u00e9t t\u00edch ba \u0111\u01a1n th\u1ee9c \u0111\u00e3 cho: <br\/> $\\begin{aligned} & \\dfrac{3}{5}{{x}^{2}}{{y}^{3}}.\\left( -2{{x}^{4}}{{y}^{2}} \\right).\\left( -\\dfrac{1}{6}{{x}^{2}}{{y}^{5}} \\right) \\\\ & =\\left[ \\dfrac{3}{5}.\\left( -2 \\right).\\left( -\\dfrac{1}{6} \\right) \\right]\\left( {{x}^{2}}{{x}^{4}}{{x}^{2}} \\right)\\left( {{y}^{3}}{{y}^{2}}{{y}^{5}} \\right) \\\\ & =\\dfrac{1}{5}{{x}^{8}}{{y}^{10}} \\\\ & Do\\,\\,\\left\\{ \\begin{aligned} & {{x}^{8}}\\ge 0\\,\\,\\forall x \\\\ & {{y}^{10}}\\ge 0\\,\\,\\forall y \\\\ \\end{aligned} \\right. \\\\ & \\Rightarrow \\dfrac{1}{5}{{x}^{8}}{{y}^{10}}\\,\\,\\ge 0\\,\\,\\,\\forall x,y \\\\ \\end{aligned}$ <br\/> Do \u0111\u00f3, ba \u0111\u01a1n th\u1ee9c: $\\dfrac{3}{5}x^2y^3; -2x^4y^2$ v\u00e0 $-\\dfrac{1}{6}x^2y^5$ kh\u00f4ng th\u1ec3 c\u00f9ng c\u00f3 gi\u00e1 tr\u1ecb \u00e2m v\u1edbi m\u1ecdi $x,y.$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang.<\/span> <\/span>","column":2}]}],"id_ques":1283},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":" <span class='basic_left'> Gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $C=(x^2-1)(x^2-2)...(x^2-2018)$ t\u1ea1i $x=5$ l\u00e0: <\/span>","select":["A. $2018$","B. $2000$","C. $1$","D. $0$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> X\u00e9t xem bi\u1ec3u th\u1ee9c $C$ c\u00f3 ch\u1ee9a th\u1eeba s\u1ed1 $x^2-25$ kh\u00f4ng?<br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Theo quy lu\u1eadt c\u1ee7a bi\u1ec3u th\u1ee9c $C$ th\u00ec $x^2-25$ l\u00e0 m\u1ed9t th\u1eeba s\u1ed1 c\u1ee7a n\u00f3. <br\/> M\u00e0 t\u1ea1i $x=5$ th\u00ec $x^2-25=5^2-25=0$ <br\/> Do \u0111\u00f3 $C=0.$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span><\/span>","column":4}]}],"id_ques":1284},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-35"],["-2"],["5"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c $A=(x+2)^2+(y-5)^2-35.$ Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t \u0111\u00f3 \u0111\u1ea1t \u0111\u01b0\u1ee3c khi n\u00e0o? <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $Min\\,A=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ khi $x=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{};y=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span>","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u0110\u00e1nh gi\u00e1 v\u00e0 nh\u1eadn \u0111\u1ecbnh $A\\ge m$ v\u1edbi $m$ l\u00e0 h\u1eb1ng s\u1ed1. <br\/> Khi \u0111\u00f3 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$ l\u00e0 $m$ <br\/> T\u00ecm \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 $A=m$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $(x+2)^2 \\ge 0$ $\\forall x$ v\u00e0 $(y-5)^2 \\ge 0$ $\\forall y$ <br\/> $\\Rightarrow A=(x+2)^2+(y-5)^2-35 \\ge -35$ v\u1edbi $\\forall x,y$ <br\/> $\\Rightarrow Min\\,A=-35$ <br\/> D\u1ea5u ''='' x\u1ea3y ra khi $\\left\\{ \\begin{align} & x+2=0 \\\\ & y-5=0 \\\\ \\end{align} \\right.$ $\\Rightarrow \\left\\{ \\begin{align} & x=-2 \\\\ & y=5 \\\\ \\end{align} \\right.$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o c\u00e1c \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $-35;-2;5$ <\/span><\/span>"}]}],"id_ques":1285},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":" <span class='basic_left'> T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $E=\\dfrac{4m-2n}{4m+5n}$ v\u1edbi $\\dfrac{m}{n}=\\dfrac{1}{5}$ ($n\\ne 0$) <\/span>","select":["A. $E=\\dfrac{18}{25}$","B. $E=-\\dfrac{21}{5}$","C. $E=\\dfrac{14}{29}$","D. $E=-\\dfrac{6}{29}$"],"hint":"T\u1eeb $\\dfrac{m}{n}=\\dfrac{1}{5}$ r\u00fat $n$ theo $m$ r\u1ed3i thay v\u00e0o $E$","explain":"<span class='basic_left'> T\u1eeb $\\dfrac{m}{n}=\\dfrac{1}{5}$ $\\Rightarrow n=5m$ <br\/> Thay $n=5m$ v\u00e0o bi\u1ec3u th\u1ee9c $E$ ta \u0111\u01b0\u1ee3c: <br\/> $E=\\dfrac{4m-2.5m}{4m+5.5m}=\\dfrac{-6m}{29m}=-\\dfrac{6}{29}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span><\/span>","column":4}]}],"id_ques":1286},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> T\u00ecm gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a bi\u1ebfn $x$ \u0111\u1ec3 bi\u1ec3u th\u1ee9c $A=\\dfrac{5}{4-x}$ c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t. <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $x=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span>","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Bi\u1ec3u th\u1ee9c $A=\\dfrac{5}{4-x}$ c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t t\u1ee9c l\u00e0 $A$ c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 s\u1ed1 nguy\u00ean d\u01b0\u01a1ng l\u1edbn nh\u1ea5t. <br\/> T\u1eeb \u0111\u00f3 t\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a $x$ th\u1ecfa m\u00e3n $A$ l\u00e0 l\u1edbn nh\u1ea5t. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> \u0110\u1ec3 $A=\\dfrac{5}{4-x}$ c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t th\u00ec $4-x$ nh\u1eadn gi\u00e1 tr\u1ecb nguy\u00ean d\u01b0\u01a1ng nh\u1ecf nh\u1ea5t. <br\/> $\\Rightarrow 4-x=1 \\Rightarrow x=3$ <br\/> V\u1eady $Max \\,A =5$ khi $x=3$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $3$ <\/span><\/span>"}]}],"id_ques":1287},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 \u0111\u00fang nh\u1ea5t v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-5"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> Cho \u0111a th\u1ee9c $A(x)=ax^4-3x^3-2ax^2+x+1$ ($a$ l\u00e0 h\u1eb1ng s\u1ed1) <br\/> H\u00e3y t\u00ecm $a$ th\u00edch h\u1ee3p \u0111\u1ec3 cho $A(x)$ c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 $4$ t\u1ea1i $x=1.$ <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $a=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span>","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Thay $x=1$ v\u00e0o $A(x)$ \u0111\u01b0a n\u00f3 v\u1ec1 \u0111a th\u1ee9c ch\u1ec9 ch\u1ee9a $a$ <br\/> Cho \u0111a th\u1ee9c thu \u0111\u01b0\u1ee3c b\u1eb1ng $4$ \u0111\u1ec3 t\u00ecm $a$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Thay $x=1$ v\u00e0o $A(x)$ ta \u0111\u01b0\u1ee3c: <br\/> $A(1)=a.1^4-3.1^3-2a.1^2+1+1=-a-1$ <br\/> Do $A(1)=4$ n\u00ean: <br\/> $-a-1=4 \\Rightarrow a=-5$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-5$ <\/span><\/span>"}]}],"id_ques":1288},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Bi\u1ebft $\\left( {{x}^{3}}-4{{x}^{2}}+2x-1 \\right)-M={{x}^{3}}-5{{x}^{2}}+4x-1$ <br\/> T\u00ecm b\u1eadc v\u00e0 h\u1ec7 s\u1ed1 t\u1ef1 do c\u1ee7a \u0111a th\u1ee9c $M.$ <\/span>","select":["A. B\u1eadc c\u1ee7a $M$ l\u00e0 $2$ v\u00e0 h\u1ec7 s\u1ed1 t\u1ef1 do c\u1ee7a n\u00f3 l\u00e0 $0$","B. B\u1eadc c\u1ee7a $M$ l\u00e0 $2$ v\u00e0 h\u1ec7 s\u1ed1 t\u1ef1 do c\u1ee7a n\u00f3 l\u00e0 $2$","C. B\u1eadc c\u1ee7a $M$ l\u00e0 $3$ v\u00e0 h\u1ec7 s\u1ed1 t\u1ef1 do c\u1ee7a n\u00f3 l\u00e0 $0$","D. B\u1eadc c\u1ee7a $M$ l\u00e0 $3$ v\u00e0 h\u1ec7 s\u1ed1 t\u1ef1 do c\u1ee7a n\u00f3 l\u00e0 $2$"],"hint":"Mu\u1ed1n t\u00ecm \u0111a th\u1ee9c tr\u1eeb ta l\u1ea5y \u0111a th\u1ee9c b\u1ecb tr\u1eeb tr\u1eeb \u0111i \u0111a th\u1ee9c hi\u1ec7u. ","explain":"<span class='basic_left'>Ta c\u00f3: <br\/> $\\begin{align} & \\left( {{x}^{3}}-4{{x}^{2}}+2x-1 \\right)-M={{x}^{3}}-5{{x}^{2}}+4x-1 \\\\ & \\Rightarrow M=\\left( {{x}^{3}}-4{{x}^{2}}+2x-1 \\right)-\\left( {{x}^{3}}-5{{x}^{2}}+4x-1 \\right) \\\\ & \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,={{x}^{3}}-4{{x}^{2}}+2x-1-{{x}^{3}}+5{{x}^{2}}-4x+1 \\\\ & \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\left( {{x}^{3}}-{{x}^{3}} \\right)+\\left( -4{{x}^{2}}+5{{x}^{2}} \\right)+\\left( 2x-4x \\right)+\\left( -1+1 \\right) \\\\ & \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,={{x}^{2}}-2x \\\\ \\end{align}$ <br\/> Do \u0111\u00f3, b\u1eadc c\u1ee7a \u0111a th\u1ee9c $M$ l\u00e0 $2$ v\u00e0 h\u1ec7 s\u1ed1 t\u1ef1 do c\u1ee7a $M$ l\u00e0 $0$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span><\/span>","column":1}]}],"id_ques":1289},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":" <span class='basic_left'> Bi\u1ebft $M-\\left( 3x-{{x}^{4}}+2{{x}^{2}}+3{{x}^{3}}-2 \\right)=2x-3{{x}^{3}}+{{x}^{4}}+2$ <br\/> C\u00e1c nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c $M$ l\u00e0: <\/span>","select":["A. $x=1$ v\u00e0 $x=-2$","B. $x=0$","C. $x=0$ v\u00e0 $x=-\\dfrac{5}{2}$","D. $x=-1$ v\u00e0 $x=-\\dfrac{5}{2}$"],"hint":"Mu\u1ed1n t\u00ecm \u0111a th\u1ee9c b\u1ecb tr\u1eeb ta l\u1ea5y \u0111a th\u1ee9c hi\u1ec7u c\u1ed9ng v\u1edbi \u0111a th\u1ee9c tr\u1eeb. ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>T\u00ecm \u0111a th\u1ee9c $M$ t\u1eeb d\u1eef ki\u1ec7n \u0111\u1ec1 b\u00e0i \u0111\u00e3 cho. <br\/> Cho $M=0$ \u0111\u1ec3 t\u00ecm nghi\u1ec7m c\u1ee7a n\u00f3. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/> $\\begin{aligned} & M-\\left( 3x-{{x}^{4}}+2{{x}^{2}}+3{{x}^{3}}-2 \\right)=2x-3{{x}^{3}}+{{x}^{4}}+2 \\\\ & \\Rightarrow M=\\left( 2x-3{{x}^{3}}+{{x}^{4}}+2 \\right)+\\left( 3x-{{x}^{4}}+2{{x}^{2}}+3{{x}^{3}}-2 \\right) \\\\ & \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=2x-3{{x}^{3}}+{{x}^{4}}+2+3x-{{x}^{4}}+2{{x}^{2}}+3{{x}^{3}}-2 \\\\ & \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\left( {{x}^{4}}-{{x}^{4}} \\right)+\\left( -3{{x}^{3}}+3{{x}^{3}} \\right)+2{{x}^{2}}+\\left( 2x+3x \\right)+\\left( 2-2 \\right) \\\\ & \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=2{{x}^{2}}+5x \\\\ & \\text{Ta c\u00f3}\\,\\, M=0 \\\\ & \\Rightarrow 2{{x}^{2}}+5x=0 \\\\ & \\Rightarrow x\\left( 2x+5 \\right)=0 \\\\ & \\Rightarrow \\left[ \\begin{aligned} & x=0 \\\\ & 2x+5=0 \\\\ \\end{aligned} \\right.\\Rightarrow \\left[ \\begin{aligned} & x=0 \\\\ & x=-\\dfrac{5}{2} \\\\ \\end{aligned} \\right. \\\\ \\end{aligned}$ <br\/> Do \u0111\u00f3, nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c $M$ l\u00e0 $x=0$ v\u00e0 $x=-\\dfrac{5}{2}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span><\/span>","column":2}]}],"id_ques":1290}],"lesson":{"save":0,"level":2}}