Chứng minh rằng với mọi số dương a,b,c,d>0" role="presentation" style="border:0px; color:rgb(0, 0, 128); direction:ltr; display:inline-block; float:none; font-family:times new roman; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-wrap:normal" class="MathJax_CHTML mjx-chtml">a,b,c,d>0$a,b,c,d>0$ thì
a−db+d+d−bb+c+b−cc+a+c−aa+d≥0" role="presentation" style="border:0px; color:rgb(0, 0, 128); direction:ltr; display:inline-block; float:none; font-family:times new roman; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-wrap:normal" class="MathJax_CHTML mjx-chtml">a−db+d+d−bb+c+b−cc+a+c−aa+d≥0$\frac{a-d}{b+d}+\frac{d-b}{b+c}+\frac{b-c}{c+a}+\frac{c-a}{a+d}\ge 0$

CMR: Với n lẻ: 
an+bn=(a+b)(an−1−an−2b+an−3b2−...+a2bn−3−abn−2+bn−1)" role="presentation" style="border:0px; color:rgb(40, 40, 40); direction:ltr; display:inline-block; float:none; font-family:helvetica,arial,sans-serif; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-wrap:normal" class="MathJax_CHTML mjx-chtml">an+bn=(a+b)(an−1−an−2b+an−3b2−...+a2bn−3−abn−2+bn−1)${\displaystyle a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+a^{n-3}{b}^2-...+a^2{b}^{n-3}-a{b}^{n-2}+b^{n-1})}$ 

Chứng minh bằng phương pháp quy nạp nhé!

Cho 2 số thực dương x,y thỏa mãn

$x^3+y^3-3xy\left(x^2+y^2\right)+4x^2{y}^2\left(x+y\right)-4x^3{y}^3=0$

Tìm giá trị nhỏ nhất của biểu thức M=x+y

Có bn nào bt lm thì giúp mk nha!!! Thanks

{x3+x−2=y3+3y2+4yx5+y3+1=0

Bài toán: Cho ba số x,y,z" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x,y,z${\displaystyle x,y,z}$ thỏa mãn x+y+z=0" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x+y+z=0${\displaystyle x+y+z=0}$ và x2+y2+z2=a2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x2+y2+z2=a2${\displaystyle x^2+y^2+z^2=a^2}$. Tính x4+y4+z4" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x4+y4+z4${\displaystyle x^4+y^4+z^4}$ theo a" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">a${\displaystyle a}$.

Giải hệ phương trình:\(\hept{ }\)
{x+10+y−1=11y+10+x−1=11" role="presentation" style="border:0px; direction:ltr; display:inline-table; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">√x+10+√y−1=11√y+10+√x−1=11

a,b>0" role="presentation" style="border:0px; color:rgb(0, 128, 128); direction:ltr; display:inline-block; float:none; font-family:fixedsys; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-wrap:normal" class="MathJax_CHTML mjx-chtml">a,b>0$a,b>0$ chứng minh :
1a3+a3b3+b3≥1a+ab+b" role="presentation" style="border:0px; color:rgb(0, 128, 128); direction:ltr; display:inline-block; float:none; font-family:fixedsys; font-size:18.18px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-wrap:normal" class="MathJax_CHTML mjx-chtml">1a3+a3b3+b3≥1a+ab+b$\frac{1}{a^3}+\frac{a^3}{b^3}+b^3\ge \frac{1}{a}+\frac{a}{b}+b$

x−2+10−x=x2−12x+40" role="presentation" style="background-color:rgb(247, 247, 247); border:0px; color:rgb(40, 40, 40); direction:ltr; display:inline-block; float:none; font-family:helvetica,arial,sans-serif; font-size:14.04px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">√x−2+√10−x=x2−12x+40${\displaystyle \sqrt{x-2}+\sqrt{10-x}=x^2-12x+40}$

giúp  mình với!!

Bài 1: Rút gọn biểu thức:
$a)\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}$
$b)\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}$
$c)\sqrt{9-2\sqrt{14}}-\sqrt{9-2\sqrt{14}}$
$d)\sqrt{2(4-\sqrt{7})}$
$e)\sqrt{a+1+2\sqrt{a}}$
$f)-\sqrt{2(2-\sqrt{3})}+\sqrt{2(2+\sqrt{3})}$
$g)\sqrt{x+y-2\sqrt{xy}}$ $(x\ge y)$
$h)\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}$
$i)\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}$
$j)\frac{\sqrt{3}+\sqrt{11+6\sqrt{2}}-\sqrt{5-2\sqrt{6}}}{\sqrt{2}+\sqrt{6+2\sqrt{5}-\sqrt{7+2\sqrt{10}}}}$
$k)\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}$
$l)\sqrt{94-42\sqrt{5}}-\sqrt{94+42\sqrt{5}}$
$m\left)\right(4+\sqrt{15}\left)\right(\sqrt{10}-\sqrt{6}\left)\right(4-\sqrt{15})$
$n\left)\sqrt{3-\sqrt{5}}\right(\sqrt{10}-\sqrt{2}\left)\right(3+\sqrt{5})$
$o)\sqrt{31+2}.\sqrt{6+\sqrt{5+\sqrt{2}}}.+\sqrt{3+\sqrt{3+\sqrt{5+\sqrt{2}}}}.\sqrt{3-\sqrt{3+\sqrt{5+\sqrt{2}}}}$

Bài 2: Phân tích đa thức thành nhân tử:
$a)x-\sqrt{x}$
$b)x-1$
$c)x-2\sqrt{2}+1$
$d)-x+3\sqrt{x}+4$
$e)2x-\sqrt{x}-1$
$f)x-\sqrt{2}-2$
$g)x\sqrt{x}+1$
$h)2x+\sqrt{x}-3$
$i)x\sqrt{x}+9x+14\sqrt{x}$
$j)2x\sqrt{x}+5x+3\sqrt{x}$

Bài 3: Cho biểu thức
$E=(\frac{3x-2}{x^2-9}-\frac{5x+1}{x^2-3x}-\frac{x+1}{x^2+3x}):\frac{x+2}{x^2+3x}-\frac{4^2-2x}{x^2-x-6}$
a) Tìm ĐKXĐ
b) Rút gọn.
c) Tìm giá trị nguyên cuả x để E nhận giá trị nguyên.

Giúp mk vs (ko hỉu j thì thôi nha )