{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"C\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc c\u1ee7a $a^2-6ab+ 9b^2$ l\u00e0:","select":["A. $a - 3b$","B. $3b -a$","C. $|a - 3b|$","D. $a^2-6ab+ 9b^2$"],"hint":"Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c v\u1ec1 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u r\u1ed3i t\u00ecm c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$a^2-6ab+ 9b^2=\\left(a - 3b \\right)^{2}$ <br\/>C\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc c\u1ee7a $a^2-6ab+ 9b^2$ l\u00e0 $\\sqrt{\\left(a - 3b \\right)^{2}}=|a - 3b|$ (v\u00ec $|a - 3b| \\ge 0$).<br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C <\/span><\/span>","column":2}]}],"id_ques":451},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai1/lv3/img\/4.jpg' \/><\/center><br\/>Gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c: $D=\\dfrac{3}{5}\\sqrt{16}+2\\sqrt{\\dfrac{16}{25}}$<br\/>\u0110\u00e1p s\u1ed1: $D= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$","hint":"","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align*} D&=\\dfrac{3}{5}\\sqrt{16}+2\\sqrt{\\dfrac{16}{25}}\\\\&=\\dfrac{3}{5}\\sqrt{{{4}^{2}}}+2\\sqrt{{{\\left( \\dfrac{4}{5} \\right)}^{2}}}\\\\&=\\dfrac{12}{5}+\\dfrac{8}{5}=4\\\\ \\end{align*}$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 ph\u1ea3i \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $4$<\/span><\/span>"}]}],"id_ques":452},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1","3"],["3","1"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"Cho $x\\ge 1$. H\u00e3y gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh sau: $\\sqrt {4x-3}=x$<br\/> \u0110\u00e1p s\u1ed1: $\\left[ \\begin{array}{} x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\end{array} \\right.$","hint":"B\u00ecnh ph\u01b0\u01a1ng hai v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> B\u00ecnh ph\u01b0\u01a1ng hai v\u1ebf.<br\/><b>B\u01b0\u1edbc 2:<\/b> Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed v\u00e0 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3:<br\/>V\u00ec $x \\ge 1$ suy ra $4x - 3 > 0$ n\u00ean:<br\/>$\\sqrt {4x-3}=x$<br\/>$\\Leftrightarrow 4x - 3={{x}^{2}}$<br\/>$\\Leftrightarrow {{x}^{2}}-4x+3=0\\,\\,$<br\/>$\\Leftrightarrow x^2 - x - 3x + 3$<br\/>$\\Leftrightarrow x (x - 1) - 3 (x - 1)$<br\/>$\\Leftrightarrow \\left( x-3 \\right)\\left( x-1 \\right)=0\\,\\,$<br\/>$\\Leftrightarrow \\,\\left[ \\begin{align}& x=3\\,\\,\\left( \\text{th\u1ecfa m\u00e3n} \\right) \\\\ & x=1\\,\\,\\left( \\text{th\u1ecfa m\u00e3n} \\right) \\\\ \\end{align} \\right.$<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S=\\{3; 1\\}$ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $1;3.$<\/span><\/span>"}]}],"id_ques":453},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"select":["A. $(\\sqrt{2}+1)^{2}$","B. $(\\sqrt{2}+2)^{2}$","C. $(\\sqrt{2}+3)^{2}$"],"ques":"H\u00e3y vi\u1ebft bi\u1ec3u th\u1ee9c $11+6\\sqrt {2}$ th\u00e0nh b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng.","hint":"T\u00e1ch $11=2+9$. V\u1eadn d\u1ee5ng h\u1eb3ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng \u0111\u1ec3 bi\u1ebfn \u0111\u1ed5i ti\u1ebfp.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$11+6\\sqrt{2}=2+6\\sqrt{2}+9={{\\left( \\sqrt{2} \\right)}^{2}}+2.3.\\sqrt{2}+{{3}^{2}}={{\\left( \\sqrt{2}+3 \\right)}^{2}}$ <br\/><\/span>"}]}],"id_ques":454},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["16"],["3"]]],"list":[{"point":10,"width":20,"content":"T\u00ednh c\u0103n b\u1eadc hai c\u1ee7a h\u1ed7n s\u1ed1 sau:","type_input":"","ques":"$\\sqrt{28\\dfrac{4}{9}}=\\dfrac{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}$","hint":"\u0110\u1ed5i h\u1ed7n s\u1ed1 ra ph\u00e2n s\u1ed1 v\u00e0 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c d\u01b0\u1edbi \u0111\u00e2y. <br\/>V\u1edbi $a\\geq 0$ th\u00ec $\\sqrt{a^2}=a$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Bi\u1ebfn \u0111\u1ed5i t\u1eeb h\u1ed7n s\u1ed1 v\u1ec1 ph\u00e2n s\u1ed1<br\/><b>B\u01b0\u1edbc 2:<\/b> V\u1edbi $a\\geq 0$ th\u00ec $\\sqrt{a^2}=a$<br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>Ta c\u00f3:<br\/>$\\sqrt{28\\dfrac{4}{9}}=\\sqrt{\\dfrac{28.9+4}{9}}=\\sqrt{\\dfrac{256}{9}}=\\sqrt{{{\\left( \\dfrac{16}{3} \\right)}^{2}}}=\\dfrac{16}{3}$<br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $\\dfrac{16}{3}$<\/span> <\/span> <\/span>"}]}],"id_ques":455},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-10"],["25"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"Cho $a \\ge0$. T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c: $A=a-10\\sqrt{a}+15$<br\/>\u0110\u00e1p s\u1ed1: $A_{\\min}=$_input_ khi $a =$ _input_","hint":"Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c v\u1ec1 d\u1ea1ng $A=[f(a)]^2+b$ d\u1ef1a v\u00e0o h\u1eb1ng \u0111\u1eb3ng th\u1ee9c.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b>T\u00e1ch $15 = 25 - 10$. Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c $A=a-10\\sqrt{a}+15=(\\sqrt{a}\u22125)^2\u221210$ <br\/><b>B\u01b0\u1edbc 2:<\/b> \u0110\u00e1nh gi\u00e1 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c $A$.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><span class='basic_left'>V\u1edbi $a \\ge 0$, ta c\u00f3:<br\/>$A=a-10\\sqrt{a}+15$<br\/>$=(\\sqrt{a})^2-2.\\sqrt{a}.5+ 5^2 -10$<br\/>$={{\\left( \\sqrt{a}-5\\right)}^{2}}-10$<br\/>V\u00ec ${{\\left( \\sqrt{a}-5 \\right)}^{2}}\\ge 0$ v\u1edbi m\u1ecdi $a \\ge 0$ <br\/>n\u00ean $A={{\\left( \\sqrt{a}-5 \\right)}^{2}}-10\\ge -10$ <br\/>Do \u0111\u00f3, ${{A}_{\\min }}=-10 \\\\ \\Leftrightarrow {{\\left( \\sqrt{a}-5 \\right)}^{2}}=0 \\\\ \\Leftrightarrow \\sqrt{a}=5 \\\\ \\Leftrightarrow a=25$ <\/span> <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng \u0111\u1ec3 $A_{\\min}=-10$ khi $a = 25$<\/span> <\/span><\/span> "}]}],"id_ques":456},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["289"],["49"]]],"list":[{"point":10,"width":20,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai1/lv3/img\/2.jpg' \/><\/center>$\\sqrt{\\dfrac{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}}=2\\dfrac{3}{7}$","hint":"Bi\u1ebfn \u0111\u1ed5i v\u1ebf ph\u1ea3i v\u1ec1 d\u1ea1ng ph\u00e2n s\u1ed1, r\u1ed3i v\u1eadn d\u1ee5ng $a=\\sqrt{a^2}$ v\u1edbi m\u1ecdi $a \\ge 0$","explain":" Ta c\u00f3: $2\\dfrac{3}{7}=\\dfrac{17}{7}=\\sqrt{{{\\left( \\dfrac{17}{7} \\right)}^{2}}}=\\sqrt{\\dfrac{289}{49}}$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $\\dfrac{289}{49}$<\/span><\/span>"}]}],"id_ques":457},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["8"],["9"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"Cho $a \\ge0$. T\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c: $A=-a+6\\sqrt{a}-1$<br\/>\u0110\u00e1p s\u1ed1: $A_{\\max}=$_input_ khi $a =$ _input_","hint":"S\u1eed d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u1ec3 bi\u1ebfn \u0111\u1ed5i $A$ v\u1ec1 d\u1ea1ng $b-[f(a)]^2$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c $A$ v\u1ec1 d\u1ea1ng $A = b - [f(a)]^2$ <br\/><b>B\u01b0\u1edbc 2:<\/b> \u0110\u00e1nh gi\u00e1 $A$ \u0111\u1ec3 t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><span class='basic_left'>V\u1edbi $a \\ge 0,$ ta c\u00f3:<br\/>$\\begin{align}A&=-a+6\\sqrt{a}-1\\\\&=-\\left( a-6\\sqrt{a}+1 \\right)\\\\&=-\\left[ (\\sqrt{a})^2-2.3\\sqrt{a}+3^2-3^2+1 \\right]\\\\&=-\\left[ {{\\left( \\sqrt{a}-3 \\right)}^{2}} - 8 \\right]\\\\&=8-{{\\left( \\sqrt{a}-3 \\right)}^{2}}\\\\ \\end{align}$<br\/>V\u00ec $-{{\\left( \\sqrt{a}-3 \\right)}^{2}}\\le 0$ v\u1edbi m\u1ecdi $a\\ge 0$ n\u00ean <br\/>$A=8-{{\\left( \\sqrt{a}-3 \\right)}^{2}}\\le 8$ v\u1edbi m\u1ecdi $a\\ge0$ <br\/>Do \u0111\u00f3 ${{A}_{\\max }}=8 \\\\ \\Leftrightarrow {{\\left( \\sqrt{a}-3 \\right)}^{2}}=0 \\\\ \\Leftrightarrow \\sqrt{a}=3 \\\\ \\Leftrightarrow a=9$ <\/span> <br\/>V\u1eady \u0111\u1ec3 $A_{\\max}= 8$ khi $a = 9$<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 $8 ; 9.$<\/span><\/span> "}]}],"id_ques":458},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["7"],["1"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"Cho a $\\ge0$. T\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c: $A=-4a+8\\sqrt{a}+3$<br\/>\u0110\u00e1p s\u1ed1: $A_{\\max}=$_input_ khi a = _input_","hint":"S\u1eed d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u1ec3 bi\u1ebfn \u0111\u1ed5i $A$ v\u1ec1 d\u1ea1ng $b-[f(a)]^2$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c $A$ v\u1ec1 d\u1ea1ng $A = b - [f(a)]^2$ <br\/><b>B\u01b0\u1edbc 2:<\/b> \u0110\u00e1nh gi\u00e1 $A$ \u0111\u1ec3 t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t. <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><span class='basic_left'>V\u1edbi $a \\ge 0,$ ta c\u00f3<br\/>$\\begin{align} A&=-4a+8\\sqrt{a}+3\\\\&=-\\left( 4a-8\\sqrt{a}-3 \\right)\\\\&=-\\left[ {{\\left( 2\\sqrt{a}-2 \\right)}^{2}}-7 \\right]\\\\&=7-{{\\left( 2\\sqrt{a}-2 \\right)}^{2}}\\\\ \\end{align}$<br\/>V\u00ec $-{{\\left( 2\\sqrt{a}- 2\\right)}^{2}}\\le 0$ v\u1edbi m\u1ecdi $a\\ge 0$ n\u00ean $A=7-{{\\left( 2\\sqrt{a}-2 \\right)}^{2}}\\le 7$v\u1edbi m\u1ecdi $a\\ge 0$ <br\/>Do \u0111\u00f3 ${{A}_{\\max }}=7 \\\\ \\Leftrightarrow {{\\left( 2\\sqrt{a}-2 \\right)}^{2}}=0 \\\\ \\Leftrightarrow \\sqrt{a}=1\\\\ \\Leftrightarrow a=1$ <\/span> <br\/> V\u1eady \u0111\u1ec3 $A_{\\max}=7$ khi $a = 1$ <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 $7 ; 1.$<\/span><\/span> "}]}],"id_ques":459},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u $> , < , =$ th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng sau","title_trans":"","temp":"fill_the_blank_random","correct":[[["<"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai1/lv3/img\/5.jpg' \/><\/center>So s\u00e1nh $1-\\dfrac{2}{\\sqrt{23}}$ _input_ $\\dfrac{3}{5}$ ","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Bi\u1ebfn \u0111\u1ed5i v\u1ec1 so s\u00e1nh $1-\\dfrac{2}{\\sqrt{23}}$ v\u00e0 $1-\\dfrac{2}{5}$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: $\\dfrac{2}{5}=\\dfrac{2}{\\sqrt{25}}$<br\/>V\u00ec $\\sqrt{23}<\\sqrt{25}\\Rightarrow \\dfrac{2}{\\sqrt{25}}<\\dfrac{2}{\\sqrt{23}}\\Rightarrow \\dfrac{2}{5}<\\dfrac{2}{\\sqrt{23}}$<br\/>Suy ra $1-\\dfrac{2}{5}>1-\\dfrac{2}{\\sqrt{23}}\\Rightarrow 1-\\dfrac{2}{\\sqrt{23}}<\\dfrac{3}{5}$<br\/> <span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $<$<\/span><\/span> "}]}],"id_ques":460}],"lesson":{"save":0,"level":3}}