\(x^5+y^5-\left(x+y\right)^5\)

\(=x^5+y^5-\left(x^5+5x^4y+10x^3y^2+10x^2y^3+8xy^4+y^5\right)\)

\(=-5xy\left(x^3+2x^2y+2xy^2+y^3\right)\)

\(=-5xy\left[\left(x+y\right)\left(x^2-xy+y^2\right)+2xy\left(x+y\right)\right]\)

\(=-5xy\left(x+y\right)\left(x^2+xy+y^2\right)\)

khó quá

\(\Rightarrow\left(3x+2\right)\left(x^2-1\right)-\left(9x^2-4\right)\left(x+1\right)=0\)

\(\Rightarrow\left(3x+2\right)\left(x+1\right)\left(x-1\right)-\left(3x+2\right)\left(3x-2\right)\left(x+1\right)=0\)

\(\Rightarrow\left(3x+2\right)\left(x+1\right)\left(x-1-3x+2\right)=0\)

\(\Rightarrow\left(3x+2\right)\left(x+1\right)\left(1-2x\right)=0\)

=> 3x + 2 = 0 => x = -2/3

hoặc x + 1 = 0 => x = -1

hoặc 1 - 2x = 0 => x = 1/2

(3x+2)(x²-1) = (9x²-4)(x+1) => (3x+2)(x-1)(x+1) = [ (3x)²- 2² ](x+1) => (3x+2)(x-1) = (3x+2)(3x-2)

=> x-1 = 3x-2 => x = 3x-1 => 1 = 3x-x = 2x => x = 1:2 = 0,5

ĐK: \(x^2-1\ge0\)

pt <=> \(\left(x^2+2x+1\right)-2\left(x+1\right)\sqrt{x^2-1}+\left(x^2-1\right)-4x^2+4x-1=0\)

<=> \(\left[\left(x+1\right)^2-2\left(x+1\right)\sqrt{x^2-1}+\left(x^2-1\right)\right]-\left(2x-1\right)^2=0\)

<=> \(\left(x+1-\sqrt{x^2-1}\right)^2-\left(2x-1\right)^2=0\)

<=> \(\left(x+1-\sqrt{x^2-1}-2x+1\right)\left(x+1-\sqrt{x^2-1}+2x-1\right)=0\)

Phương trình tích. Dễ rồi đúng ko? Tự làm tiếp nhé!

\(\hept{\begin{cases}7\left(2x+y\right)-5\left(3x+y\right)=6\\3\left(x+2y\right)-2\left(x+3y\right)=-6\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}14x+7y-15x-5y=6\\3x+6y-2x-6y=-6\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}-x+2y=6\\x=-6\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=-6\\y=0\end{cases}}\)

xét x=0 thấy không là nghiệm

xét x khác 0; đặt x=a; \(\frac{x}{x-1}=b;=>\frac{1}{a}+\frac{1}{b}=1< =>a+b=ab.\)

a³+b³+3ab-2=0<=> (a+ b)[(a+b)²- 3ab] + 3ab - 2=0 <=> ab(a²b²- 3ab)+ 3ab- 2=0 

<=> (ab)³- 3(ab)² + 3ab - 2=0 <=> (ab- 1)³ -1 =0 <=> ab- 1 = 1 <=> ab= 2 <=> \(x.\frac{x}{x-1}=2< =>x^2=2x-2< =>x^2-2x+2=0\)(vô nghiệm) 

vậy pt vô nghiệm

b, \(x^3+3x^2y-4y^3+x-y=0\)

\(\Leftrightarrow x^3-x^2y+4x^2y-4xy^2+4xy^2-4y^3+x-y=0\)

\(\Leftrightarrow x^2\left(x-y\right)+4xy\left(x-y\right)+4y^2\left(x-y\right)+\left(x-y\right)=0\)

\(\Leftrightarrow\left(x-y\right)\left(x^2+4xy+4y^2+1\right)=0\)

\(\Leftrightarrow x-y=0\Leftrightarrow x=y\)

Khi đó pt (2) của hệ trở thành: 

\(\left(x^2+3x+2\right)\left(x^2+7x+12\right)=24\)

\(\Leftrightarrow\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)=24\)

\(\Leftrightarrow\left(x^2+5x+4\right)\left(x^2+5x+6\right)=24\)

\(\Leftrightarrow\left(x^2+5x+5\right)^2-1=24\)

\(\Leftrightarrow\left(x^2+5x+5\right)^2-5^2=0\)

\(\Leftrightarrow\left(x^2+5x\right)\left(x^2+5x+10\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=-5\end{cases}}\)

Vậy hệ có nghiệm \(\left(x;y\right)\in\left\{\left(0;0\right),\left(-5;-5\right)\right\}\)