{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"<span class='basic_left'>V\u1edbi $x \\ge 0$ v\u00e0 $x \\ne 9$. Cho bi\u1ec3u th\u1ee9c: <br\/>$M= \\left( \\dfrac{1}{\\sqrt{x}+3}+\\dfrac{\\sqrt{x}+9}{x-9} \\right).\\dfrac{\\sqrt{x}}{2}$<br\/><b> C\u00e2u 1: <\/b> R\u00fat g\u1ecdn $M$ \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 l\u00e0:<\/span> ","select":["A. $\\dfrac{\\sqrt{x}}{2(\\sqrt{x}+3)}$ ","B. $\\dfrac{\\sqrt{x}}{2(\\sqrt{x}-3)}$","C. $\\dfrac{\\sqrt{x}}{\\sqrt{x}+3}$","D. $\\dfrac{\\sqrt{x}}{\\sqrt{x}-3}$"],"hint":"Quy \u0111\u1ed3ng c\u00e1c ph\u00e2n th\u1ee9c trong ngo\u1eb7c v\u00e0 r\u00fat g\u1ecdn","explain":"<span class='basic_left'>V\u1edbi $x \\ge 0$ v\u00e0 $x \\ne 9$. Ta c\u00f3:<br\/>$\\begin{align} M&= \\left( \\dfrac{1}{\\sqrt{x}+3}+\\dfrac{\\sqrt{x}+9}{x-9} \\right).\\dfrac{\\sqrt{x}}{2} \\\\ & =\\left[ \\dfrac{\\sqrt{x}-3+\\sqrt{x}+9}{\\left( \\sqrt{x}-3 \\right)\\left( \\sqrt{x}+3 \\right)} \\right].\\dfrac{\\sqrt{x}}{2} \\\\ & =\\dfrac{2\\sqrt{x}+6}{\\left( \\sqrt{x}-3 \\right)\\left( \\sqrt{x}+3 \\right)}.\\dfrac{\\sqrt{x}}{2} \\\\ & =\\dfrac{2\\left( \\sqrt{x}+3 \\right)}{\\left( \\sqrt{x}-3 \\right)\\left( \\sqrt{x}+3 \\right)}.\\dfrac{\\sqrt{x}}{2} \\\\ & =\\dfrac{\\sqrt{x}}{\\sqrt{x}-3} \\\\ \\end{align}$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span>","column":2}]}],"id_ques":711},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"fill_the_blank","correct":[[["-2"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>V\u1edbi $x \\ge 0$ v\u00e0 $x \\ne 9$. Cho bi\u1ec3u th\u1ee9c: <br\/>$\\, M= \\left( \\dfrac{1}{\\sqrt{x}+3}+\\dfrac{\\sqrt{x}+9}{x-9} \\right).\\dfrac{\\sqrt{x}}{2}$<br\/><b> C\u00e2u 2: <\/b> V\u1edbi $x= 4$ th\u00ec $M=$_input_<\/span>","hint":"Thay $x= 4$ v\u00e0o bi\u1ec3u th\u1ee9c $M$","explain":"<span class='basic_left'>Theo c\u00e2u 1, v\u1edbi $x \\ge 0$ v\u00e0 $x \\ne 9$. Ta c\u00f3:<br\/> $M=\\dfrac{\\sqrt{x}}{\\sqrt{x}-3}$<br\/>Thay $ x=4$ v\u00e0o bi\u1ec3u th\u1ee9c $M$ ta c\u00f3:<br\/> $M=\\dfrac{\\sqrt{4}}{\\sqrt{4}-3}=\\dfrac{2}{2-3}=-2$ <br\/>V\u1eady $x=4$ th\u00ec $M= -2$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-2$<\/span><\/span>"}]}],"id_ques":712},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank_random","correct":[[["0"],["4"],["16"],["36"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>V\u1edbi $x\\ge 0$ v\u00e0 $x \\ne 9$. Cho bi\u1ec3u th\u1ee9c: <br\/>$M= \\left( \\dfrac{1}{\\sqrt{x}+3}+\\dfrac{\\sqrt{x}+9}{x-9} \\right).\\dfrac{\\sqrt{x}}{2}$<br\/><b> C\u00e2u 3: <\/b> T\u00ecm $x\\in \\mathbb Z $ \u0111\u1ec3 $M \\in \\mathbb Z$<br\/>\u0110\u00e1p \u00e1n: $x\\in$ {_input_;_input_;_input_;_input_} <br\/> $\\,\\,\\,$(C\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a $x$ vi\u1ebft theo th\u1ee9 t\u1ef1 t\u0103ng d\u1ea7n)<\/span>","hint":"Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c v\u1ec1 d\u1ea1ng: $m+\\dfrac {n}{f(x)}$ v\u1edbi $m,n \\in \\mathbb Z$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: T\u00ecm \u0111i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh c\u1ee7a bi\u1ec3u th\u1ee9c.<br\/>B\u01b0\u1edbc 2: Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c v\u1ec1 d\u1ea1ng: $m+\\dfrac {n}{f(x)}$ v\u1edbi $m,n \\in \\mathbb Z$<br\/>B\u01b0\u1edbc 3: T\u00ecm $x$ th\u1ecfa m\u00e3n $f(x)\\in \u01af(n)$<br\/>B\u01b0\u1edbc 4: T\u00ecm $x$ v\u00e0 so s\u00e1nh v\u1edbi \u0111i\u1ec1u ki\u1ec7n v\u00e0 k\u1ebft lu\u1eadn <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><span class='basic_left'> Theo c\u00e2u 1, v\u1edbi $x \\ge 0$ v\u00e0 $x \\ne 9$. Ta c\u00f3:<br\/> $M=\\dfrac{\\sqrt{x}}{\\sqrt{x}-3}$<br\/>$M=\\dfrac{\\sqrt{x}}{\\sqrt{x}-3}=1+\\dfrac{3}{\\sqrt{x}-3}$ <br\/>$M\\in \\mathbb Z\\Leftrightarrow 1+\\dfrac{3}{\\sqrt{x}-3}\\in \\mathbb Z\\,$$\\Leftrightarrow \\dfrac{3}{\\sqrt{x}-3}\\in \\mathbb Z$ <br\/>$\\Leftrightarrow \\sqrt{x}-3$ thu\u1ed9c $\u01af(3)=\\{\\pm 1;\\pm 3 \\}$<br\/>Ta c\u00f3 b\u1ea3ng sau:<br\/><table> <tr> <th>$\\sqrt{x}-3$<\/th> <th>$-3$<\/th> <th>$-1$<\/th> <th>$1$<\/th> <th>$3$<\/th> <\/tr> <tr> <td>$\\sqrt{x}$<\/td> <td>$0$<\/td> <td>$2$<\/td> <td>$4$<\/td> <td>$6$<\/td> <\/tr> <tr> <td>$x$<\/td> <td>$0$<\/td> <td>$4$<\/td> <td>$16$<\/td> <td>$36$<\/td> <\/tr><\/table><br\/>K\u1ebft h\u1ee3p v\u1edbi \u0111i\u1ec1u ki\u1ec7n $x \\ge 0$ v\u00e0 $x \\ne 9$, suy ra: $x\\in\\{0,4,16,36\\}$<br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $0;4;16;36$<\/span><\/span><\/span>"}]}],"id_ques":713},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c $2{{y}^{2}}\\sqrt{\\dfrac{{{x}^{4}}}{4{{y}^{2}}}}$ v\u1edbi $y < 0$ \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 l\u00e0: ","select":["A. $\u2013 xy^2$ ","B. $\\dfrac{{{y}^{2}}{{x}^{2}}}{\\left| y \\right|}$","C. $-x^2y$","D. $\\sqrt{{{y}^{2}}{{x}^{4}}}$"],"hint":"\u00c1p d\u1ee5ng v\u1edbi $A$ l\u00e0 m\u1ed9t bi\u1ec3u th\u1ee9c, ta c\u00f3 $\\sqrt{A^2}=|A|=\\left\\{ \\begin{align} & A\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,{A}\\ge {0} \\\\ & -A\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,{A}<{0} \\\\\\end{align} \\right.$ ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$2{{y}^{2}}\\sqrt{\\dfrac{{{x}^{4}}}{4{{y}^{2}}}}=2{{y}^{2}}\\sqrt{{{\\left( \\dfrac{{{x}^{2}}}{2y} \\right)}^{2}}}\\,$$=2{{y}^{2}}.\\left| \\dfrac{{{x}^{2}}}{2y} \\right|=2{{y}^{2}}.\\left( -\\dfrac{{{x}^{2}}}{2y} \\right)\\,$$=-{{x}^{2}}y$ (V\u00ec $y < 0$ n\u00ean $|y|=-y$)<br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span>","column":2}]}],"id_ques":714},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"select":["A. $\\sqrt{5}$","B. $2\\sqrt{5}$","C. $3\\sqrt{5}$","D. $4\\sqrt{5}$"],"ques":"R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c: <br\/>$\\sqrt{{{\\left( \\sqrt{6}+\\sqrt{5} \\right)}^{2}}}-\\sqrt{{{\\left( \\sqrt{6}-\\sqrt{5} \\right)}^{2}}} = ?$","hint":"\u00c1p d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c $\\sqrt {A^2}=|A|$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align} & \\,\\,\\,\\sqrt{{{\\left( \\sqrt{6}+\\sqrt{5} \\right)}^{2}}}-\\sqrt{{{\\left( \\sqrt{6}-\\sqrt{5} \\right)}^{2}}} \\\\ & =\\left| \\sqrt{6}+\\sqrt{5} \\right|-\\left| \\sqrt{6}-\\sqrt{5} \\right| \\\\ & =\\sqrt{6}+\\sqrt{5}-\\left( \\sqrt{6}-\\sqrt{5} \\right)\\,\\,(V\u00ec\\,\\sqrt{6}>\\sqrt{5}) \\\\ & =\\sqrt{6}+\\sqrt{5}-\\sqrt{6}+\\sqrt{5} \\\\ & =2\\sqrt{5} \\\\ \\end{align}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $2\\sqrt{5}$<\/span><br\/><i>Ghi nh\u1edb:<\/i> V\u1edbi $A$ l\u00e0 m\u1ed9t bi\u1ec3u th\u1ee9c, ta c\u00f3 $\\sqrt{A^2}=|A|=\\left\\{ \\begin{align} & A\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,{A}\\ge {0} \\\\ & -A\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,{A}<{0} \\\\\\end{align} \\right.$<\/span> "}]}],"id_ques":715},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank","correct":[[["-6"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh: <br\/>$\\,\\dfrac{4}{1+\\sqrt{3}}-\\dfrac{2}{2-\\sqrt{3}} =$_input_","hint":"Tr\u1ee5c c\u0103n th\u1ee9c \u1edf m\u1eabu","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: Tr\u1ee5c c\u0103n th\u1ee9c \u1edf m\u1eabu<br\/>V\u1edbi c\u00e1c bi\u1ec3u th\u1ee9c $A, B, C$ m\u00e0 $A\\ge0$ v\u00e0 $A\\ne {{B}^{2}}$ ta c\u00f3: $\\,\\,\\dfrac{C}{\\sqrt{A}\\pm B}=\\dfrac{C\\left( \\sqrt{A}\\mp B \\right)}{A-{{B}^{2}}}$ <br\/>B\u01b0\u1edbc 2: C\u1ed9ng tr\u1eeb c\u00e1c c\u0103n th\u1ee9c \u0111\u1ed3ng d\u1ea1ng<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3:<br\/>$\\begin{align} & \\,\\,\\,\\,\\dfrac{4}{1+\\sqrt{3}}-\\dfrac{2}{2-\\sqrt{3}} \\\\ & =\\dfrac{4(\\sqrt{3}-1)}{\\sqrt{{{3}^{2}}}-1}-\\dfrac{2(2+\\sqrt{3})}{4-\\sqrt{{{3}^{2}}}} \\\\ & =\\dfrac{4(\\sqrt{3}-1)}{2}-\\dfrac{2(2+\\sqrt{3})}{1} \\\\ & =2\\sqrt{3}-2-4-2\\sqrt{3} \\\\ & =-6 \\\\\\end{align}$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-6$<\/span> <\/span><\/span>"}]}],"id_ques":716},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank","correct":[[["5"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai7/lv1/img\/4.jpg' \/><\/center>T\u00ednh: $\\,\\,\\,\\dfrac{\\sqrt{275}}{\\sqrt{11}}=$_input_","hint":"\u00c1p d\u1ee5ng v\u1edbi $a \\ge 0$ v\u00e0 $b> 0$ ta c\u00f3 $\\dfrac{\\sqrt{a}}{\\sqrt{b}}=\\sqrt{\\dfrac{a}{b}}$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\dfrac{\\sqrt{275}}{\\sqrt{11}}$ = $\\sqrt{\\dfrac{275}{11}}=\\sqrt{25}=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":717},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank","correct":[[["1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c:<br\/>$C=\\sqrt[3]{\\sqrt{5}+2}.\\sqrt[3]{\\sqrt{5}-2}$ <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $C=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} $","hint":"\u00c1p d\u1ee5ng: $\\sqrt[3]{a}.\\sqrt[3]{b}=\\sqrt[3]{ab}$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$C=\\sqrt[3]{\\sqrt{5}+2}.\\sqrt[3]{\\sqrt{5}-2}\\,$<br\/>$=\\sqrt[3]{\\left( \\sqrt{5}+2 \\right)\\left( \\sqrt{5}-2 \\right)}\\,$<br\/>$=\\sqrt[3]{5-4}$<br\/>$=1$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $1$<\/span><\/span>"}]}],"id_ques":718},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank","correct":[[["61"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai7/lv1/img\/9.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh $\\sqrt[3]{2x+3}=5$<br\/>T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S= ${_input_}","hint":"L\u1eadp ph\u01b0\u01a1ng hai v\u1ebf","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align}&\\sqrt[3]{2x+3}\\,\\,=5\\\\&\\Leftrightarrow 2x+3=125\\\\&\\Leftrightarrow2x=122 \\\\&\\Leftrightarrow x\\,\\,\\,=61\\\\\\end{align}$<br\/>T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S=\\{61\\}$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $61$<\/span><\/span>"}]}],"id_ques":719},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank_random","correct":[[["-1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c:<br\/>$A =2x-\\sqrt{{{x}^{2}}+x+\\dfrac{1}{4}}$ t\u1ea1i $x=-\\dfrac{1}{2}$<br\/>\u0110\u00e1p s\u1ed1: $A=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} $","hint":"\u0110\u01b0a bi\u1ec3u th\u1ee9c trong c\u0103n v\u1ec1 d\u1ea1ng $(A+B)^2$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: \u0110\u01b0a bi\u1ec3u th\u1ee9c ${x}^{2}+x+\\dfrac{1}{4}$ v\u1ec1 d\u1ea1ng $(a + b)^2$<br\/>B\u01b0\u1edbc 2: \u00c1p d\u1ee5ng $\\sqrt {A^2}=|A|$ \u0111\u1ec3 khai c\u0103n<br\/>B\u01b0\u1edbc 3: Thay $x$ v\u00e0o bi\u1ec3u th\u1ee9c $A$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>$\\begin{align} A & =2x-\\sqrt{{{x}^{2}}+x+\\dfrac{1}{4}} \\\\ & =2x-\\sqrt{{{\\left( x+\\dfrac{1}{2} \\right)}^{2}}} \\\\ & =2x-\\left| x+\\dfrac{1}{2} \\right| \\\\ \\end{align}$ <br\/>Thay $x=-\\dfrac{1}{2}$ v\u00e0o bi\u1ec3u th\u1ee9c $A$ ta c\u00f3:<br\/>$A=2.\\left( -\\dfrac{1}{2} \\right)-\\left| -\\dfrac{1}{2}+\\dfrac{1}{2} \\right|=-1$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-1$<\/span><\/span><\/span>"}]}],"id_ques":720},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["f","t","t"]],"list":[{"point":5,"image":"https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai7/lv1/img\/1.png","col_name":["","\u0110\u00fang","Sai"],"arr_ques":["C\u0103n b\u1eadc hai c\u1ee7a $16$ l\u00e0 $4$ ","V\u1edbi hai s\u1ed1 $a$ v\u00e0 $b$ kh\u00f4ng \u00e2m, n\u1ebfu $a < b$ th\u00ec $\\sqrt{a}<\\sqrt{b}$","$\\sqrt{x+1}$ x\u00e1c \u0111\u1ecbnh khi $x \\ge - 1$"],"hint":"D\u1ef1a v\u00e0o \u0111\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a c\u0103n b\u1eadc hai","explain":["Sai ,v\u00ec $16$ c\u00f3 hai c\u0103n b\u1eadc hai l\u00e0 $4$ v\u00e0 $-4$","<br\/>\u0110\u00fang, v\u00ec v\u1edbi hai s\u1ed1 $a$ v\u00e0 $b$ kh\u00f4ng \u00e2m, n\u1ebfu a $< b$ th\u00ec $\\sqrt{a}<\\sqrt{b}$","<br\/>\u0110\u00fang, v\u00ec \u0111i\u1ec1u ki\u1ec7n: $x+1 \\ge \\Leftrightarrow x \\ge -1$"]}]}],"id_ques":721},{"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":"T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh $\\sqrt{\\dfrac{x}{9}}-\\sqrt{4x}=-5$ l\u00e0: ","select":["A. $S=\\{9\\}$","B. $S=\\{\\sqrt{3}\\}$","C. $S=\\{3\\}$","D. $S=\\left\\{\\dfrac{9}{7}\\right\\}$"],"hint":"\u00c1p d\u1ee5ng: Quy t\u1eafc \u0111\u01b0a th\u1eeba s\u1ed1 ra ngo\u00e0i d\u1ea5u c\u0103n ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: T\u00ecm \u0111i\u1ec1u ki\u1ec7n ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 ngh\u0129a<br\/>B\u01b0\u1edbc 2: Bi\u1ebfn \u0111\u1ed5i ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 d\u1ea1ng $\\sqrt{A}=B\\Leftrightarrow A=B^2$ v\u00e0 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<br\/><\/span>\u0110i\u1ec1u ki\u1ec7n: $x\\ge 0$<br\/>Ta c\u00f3:<br\/>$\\begin{align} & \\,\\,\\,\\sqrt{\\dfrac{x}{9}}-\\sqrt{4x}=\\,\\,-5 \\\\ & \\Leftrightarrow \\dfrac{\\sqrt{x}}{3}-2\\sqrt{x}=-5 \\\\ & \\Leftrightarrow -5\\sqrt{x}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=-15 \\\\ & \\Leftrightarrow \\sqrt{x}=3 \\\\ & \\Leftrightarrow x\\,\\,\\,\\,\\,=9 \\\\ \\end{align}$ <br\/>V\u1eady ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 t\u1eadp nghi\u1ec7m $S=\\{9\\}$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span>","column":2}]}],"id_ques":722},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"select":["A. $2\\sqrt{x}$","B. $\\sqrt{x}$","C. $-\\sqrt{x}$"],"ques":"<span class='basic_left'>Cho bi\u1ec3u th\u1ee9c $P =\\left( \\dfrac{\\sqrt{x}}{\\sqrt{x}-4}+\\dfrac{\\sqrt{x}}{\\sqrt{x}+4} \\right):\\dfrac{2\\sqrt{x}}{x-16}$ (v\u1edbi $x>0$ v\u00e0 $x\\ne 16$)<br\/><b>C\u00e2u 1: <\/b>R\u00fat g\u1ecdn $P$<br\/>\u0110\u00e1p s\u1ed1:$P=$?<\/span>","hint":"R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c trong ngo\u1eb7c tr\u01b0\u1edbc: M\u1eabu th\u1ee9c chung $(\\sqrt{x}+4 )(\\sqrt{x}-4)$ ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: T\u00ecm \u0111i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh c\u1ee7a $P$<br\/> B\u01b0\u1edbc 2: Ph\u00e2n t\u00edch m\u1eabu th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed, quy \u0111\u1ed3ng v\u00e0 r\u00fat g\u1ecdn $P$ <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>V\u1edbi $x>0$ v\u00e0 $x\\ne 16$ ta c\u00f3:<br\/>$\\left( \\dfrac{\\sqrt{x}}{\\sqrt{x}-4}+\\dfrac{\\sqrt{x}}{\\sqrt{x}+4} \\right):\\dfrac{2\\sqrt{x}}{x-16}$<br\/>$= \\left[ \\dfrac{\\sqrt{x}(\\sqrt{x}+4)}{(\\sqrt{x}-4)\\left( \\sqrt{x}+4 \\right)}+\\dfrac{\\sqrt{x}\\left( \\sqrt{x}-4 \\right)}{(\\sqrt{x}+4)\\left( \\sqrt{x}-4 \\right)} \\right]\\,$$:\\dfrac{2\\sqrt{x}}{x-16}$<br\/>$=\\left[ \\dfrac{\\sqrt{x}(\\sqrt{x}+4)+\\sqrt{x}\\left( \\sqrt{x}-4 \\right)}{(\\sqrt{x}-4)\\left( \\sqrt{x+4} \\right)} \\right]\\,$$:\\dfrac{2\\sqrt{x}}{x-16}$<br\/>$=\\dfrac{x+4\\sqrt{x}+x-4\\sqrt{x}}{x-16}.\\dfrac{x-16}{2\\sqrt{x}}$<br\/>$= \\dfrac{2x}{2\\sqrt{x}}=\\sqrt{x}$<\/span><\/span>"}]}],"id_ques":723},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["4"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Cho bi\u1ec3u th\u1ee9c $P = \\left( \\dfrac{\\sqrt{x}}{\\sqrt{x}-4}+\\dfrac{\\sqrt{x}}{\\sqrt{x}+4} \\right):\\dfrac{2\\sqrt{x}}{x-16}$ (v\u1edbi $x>0$ v\u00e0 $x \\ne 16$)<br\/><b> C\u00e2u 2: <\/b> V\u1edbi $P=2$ th\u00ec $x=$_input_<\/span>","hint":"Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh $P=2$","explain":"<span class='basic_left'>Theo c\u00e2u 1, v\u1edbi $x>0$ v\u00e0 $x \\ne 16$, ta c\u00f3: $P=\\sqrt{x}$ <br\/>Ta c\u00f3:<br\/>$P = 2 \\Leftrightarrow \\sqrt{x}=2\\Leftrightarrow x=4$ (th\u1ecfa m\u00e3n) <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $4$<\/span><\/span>"}]}],"id_ques":724},{"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":"K\u1ebft qu\u1ea3 ph\u00e9p t\u00ednh $\\dfrac{2+\\sqrt{2}}{\\sqrt{2}+1}:\\dfrac{3-\\sqrt{3}}{\\sqrt{3}-1}$ l\u00e0: ","select":["A. $\\dfrac{\\sqrt{6}}{3}$ ","B. $\\dfrac{-3}{\\sqrt{6}}$","C. $\\dfrac{-\\sqrt{6}}{3}$","D. $\\dfrac{-\\sqrt{6}}{6}$ "],"hint":"Ph\u00e2n t\u00edch t\u1eed th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed r\u1ed3i r\u00fat g\u1ecdn.","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align}&\\,\\,\\,\\,\\,\\dfrac{2+\\sqrt{2}}{\\sqrt{2}+1}:\\dfrac{3-\\sqrt{3}}{\\sqrt{3}-1}\\\\&=\\dfrac{\\sqrt{2}\\left( \\sqrt{2}+1 \\right)}{\\sqrt{2}+1}.\\dfrac{\\sqrt{3}-1}{\\sqrt{3}\\left( \\sqrt{3}-1 \\right)}\\\\&=\\dfrac{\\sqrt{2}}{\\sqrt{3}}\\\\ &=\\dfrac{\\sqrt{6}}{3}\\\\ \\end{align}$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span>","column":2}]}],"id_ques":725},{"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":"T\u00ecm $x$ \u0111\u1ec3 bi\u1ec3u th\u1ee9c $\\sqrt{\\dfrac{4}{-7+x}}$ c\u00f3 ngh\u0129a: ","select":["A. $x\\le 7$ ","B. $x\\ge 7$","C. $x > 7$","D. $x< 7$"],"hint":"$\\sqrt{\\dfrac{1}{A}}$ c\u00f3 ngh\u0129a $\\Leftrightarrow A > 0$ ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>\u0110i\u1ec1u ki\u1ec7n: $-7+x > 0 \\Leftrightarrow x > 7$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span>","column":2}]}],"id_ques":726},{"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":"V\u1edbi $x\\ge 0$. K\u1ebft qu\u1ea3 ph\u00e2n t\u00edch $6-\\sqrt{x}+36-x$ th\u00e0nh nh\u00e2n t\u1eed l\u00e0: ","select":["A. $\\left( \\sqrt{x} -6\\right)\\left( 4+\\sqrt{x} \\right)$ ","B. $\\left( 6-\\sqrt{x} \\right)\\left( 4+\\sqrt{x} \\right)$","C. $\\left( \\sqrt{x}-6 \\right)\\left( 7+\\sqrt{x} \\right)$","D. $\\left( 6-\\sqrt{x} \\right)\\left( 7+\\sqrt{x} \\right)$"],"explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,6-\\sqrt{x}+36-x\\\\ & =\\left( 6-\\sqrt{x} \\right)+\\left( 6-\\sqrt{x} \\right)\\left( 6+\\sqrt{x} \\right) \\\\ & =\\left( 6-\\sqrt{x} \\right)\\left( 7+\\sqrt{x} \\right) \\\\\\end{align}$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span>","column":2}]}],"id_ques":727},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank_random","correct":[[["2","-1"],["-1","2"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $\\sqrt{{{\\left( 2x-1 \\right)}^{2}}}=3$<br\/>T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S=${_input_;_input_}","hint":"\u0110\u01b0a th\u1eeba s\u1ed1 ra ngo\u00e0i d\u1ea5u c\u0103n \u1edf v\u1ebf tr\u00e1i c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>\u00c1p d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c: $\\sqrt {A^2}=|A|$<br\/> Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh $|A| = 0$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3:<br\/>$\\begin{align} & \\sqrt{{{\\left( 2x-1 \\right)}^{2}}}=3 \\\\ & \\Leftrightarrow \\left| 2x-1 \\right|=3 \\\\ & \\Leftrightarrow \\left[ \\begin{matrix} 2x-1=3 \\\\ 2x-1=-3 \\\\\\end{matrix} \\right. \\\\ & \\Leftrightarrow \\left[ \\begin{matrix} 2x=4 \\\\ 2x=-2 \\\\\\end{matrix} \\right. \\\\ & \\Leftrightarrow \\left[ \\begin{matrix} x=2 \\\\ x=-1 \\\\\\end{matrix} \\right. \\\\ \\end{align}$<br\/>T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 l\u00e0 $S=\\left\\{ 2;-1 \\right\\}$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $2; -1$<\/span><\/span><\/span>"}]}],"id_ques":728},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $15\\sqrt{2}$","B. $12\\sqrt{2}$","C. $10\\sqrt{2}$"],"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai7/lv1/img\/2.jpg' \/><\/center> R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c sau:<br\/>$3\\sqrt{5}-\\sqrt{45}+3\\sqrt{18}+\\sqrt{72}$=?","hint":"\u00c1p d\u1ee5ng quy t\u1eafc \u0111\u01b0a th\u1eeba s\u1ed1 ra ngo\u00e0i d\u1ea5u c\u0103n ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: \u00c1p d\u1ee5ng quy t\u1eafc \u0111\u01b0a th\u1eeba s\u1ed1 ra ngo\u00e0i d\u1ea5u c\u0103n <br\/>V\u1edbi $B\\ge 0$ ta c\u00f3 $\\sqrt{{{A}^{2}}B}=\\left| A \\right|\\sqrt{B}\\,$$=\\left\\{ \\begin{align} & \\begin{matrix} \\,\\,\\,A\\sqrt{B} & \\text {n\u1ebfu}\\,\\,\\, A\\ge0 \\\\\\end{matrix} \\\\ & \\begin{matrix} -A\\sqrt{B} & \\text {n\u1ebfu} \\,\\,\\,A < 0 \\\\\\end{matrix} \\\\ \\end{align} \\right.$<br\/> B\u01b0\u1edbc 2: C\u1ed9ng tr\u1eeb c\u00e1c c\u0103n th\u1ee9c \u0111\u1ed3ng d\u1ea1ng <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\,3\\sqrt{5}-\\sqrt{45}+3\\sqrt{18}+\\sqrt{72} \\\\ & =3\\sqrt{5}-\\sqrt{9.5}+3\\sqrt{9.2}+\\sqrt{36.2} \\\\ & =3\\sqrt{5}-3\\sqrt{5}+9\\sqrt{2}+6\\sqrt{2} \\\\ & =15\\sqrt{2} \\\\ \\end{align}$<\/span><\/span>"}]}],"id_ques":729},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank_random","correct":[[["-1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai7/lv1/img\/1.png' \/><\/center>T\u00ednh : $\\,\\,\\,\\sqrt[3]{-0,5}.\\sqrt[3]{1,25}.\\sqrt[3]{\\dfrac{16}{10}}$=_input_","hint":"\u00c1p d\u1ee5ng $\\sqrt[3]{a}.\\sqrt[3]{b}=\\sqrt[3]{ab}$ ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\sqrt[3]{-0,5}.\\sqrt[3]{1,25}.\\sqrt[3]{\\dfrac{16}{10}}=\\sqrt[3]{-0,5.1,25.\\dfrac{16}{10}}=\\sqrt[3]{\\dfrac{-5}{10}.\\dfrac{125}{100}.\\dfrac{16}{10}}=\\sqrt[3]{-1}=-1$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-1$<\/span><\/span>"}]}],"id_ques":730}],"lesson":{"save":0,"level":1}}