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

\(\Rightarrow\orbr{\begin{cases}x+1=0\\y-2=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=0-1\\y=0+2\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=-1\\y=2\end{cases}}\)

Vậy x = - 1 ; y = 2

giusp mình nhé mình đang cần lắm

Cộng 3 đẳng thức vế với vế ta có:

(x+y+z)(x+y+z)=-5+9+5

(x+y+z)²=9

=>x+y+z=3 hoặc x+y+z=-3

Với x+y+z=3 =>\(\hept{\begin{cases}3x=-5\\3y=9\\3z=5\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{-5}{3}\\y=3\\z=\frac{5}{3}\end{cases}}}\)

Với x+y+z=-3 => x=5/3,y=-3,z=-5/3

Vậy...

Ta có: \(\dfrac{y-z}{\left(x-y\right)\left(x-z\right)}=\dfrac{y-x+x-z}{\left(x-y\right)\left(x-z\right)}\)\(=\dfrac{y-x}{\left(x-y\right)\left(x-z\right)}+\dfrac{x-z}{\left(x-y\right)\left(x-z\right)}\) \(=\dfrac{1}{z-x}+\dfrac{1}{x-y}\)

Tương tự:

\(\dfrac{z-x}{\left(y-z\right)\left(y-x\right)}=\dfrac{1}{x-y}+\dfrac{1}{y-z}\)

\(\dfrac{x-y}{\left(z-x\right)\left(z-y\right)}=\dfrac{1}{y-z}+\dfrac{1}{z-x}\)

\(\Rightarrow\dfrac{y-z}{\left(x-y\right)\left(x-z\right)}+\dfrac{z-x}{\left(y-z\right)\left(y-x\right)}+\dfrac{x-y}{\left(z-x\right)\left(z-y\right)}\) \(=\dfrac{2}{x-y}+\dfrac{2}{y-z}+\dfrac{2}{z-x}\) \(\left(đpcm\right)\)

vì x + 2 = y + 1 = z + 3 => x = y - 1 = z + 1 ; y = x + 1 = z + 2; z = x + 1 = y - 2  và z < x < y

ta có (x-1/3).(y-1/2).(z-5)=0 => ta có 3 TH

TH₁ z - 5 = 0 => z = 5 ; y = 7 ; x = 4

TH₂ x - 1/3 = 0 => x = 1/3 ; y = 4/3 ; z = -2/3

TH₃ y - 1/2 = 0 => y = 1/2 ; x = -1/2 ; z = -3/2

nhớ cho mik nha 

Ta có:

\(\left(x-\frac{1}{2}\right).\left(y-\frac{1}{2}\right).\left(z-5\right)=0\)

\(\Rightarrow x-\frac{1}{2}=0;y-\frac{1}{2}=0\)hoặc \(z-5=0\)

Với \(x-\frac{1}{3}=0\Rightarrow x=\frac{1}{3}\)\(\Rightarrow\)\(x+2=\frac{1}{3}+2=\frac{7}{3}=y+1=z+3\)\(\Rightarrow y=...;z=...\)

Với \(y-\frac{1}{2}=0\Rightarrow y=\frac{1}{2}\)\(\Rightarrow....\)

Với \(z-5=0\)\(\Rightarrow.....\)

B tự làm nốt nhé

nhớ k nha

\(M=\frac{z^5.\left(x+y^2\right).\left(x^2-y^3\right).\left(x^2-y\right)}{x^2+y^2+z^2+1}=\frac{\left(-5\right)^5.\left(-4+16^2\right).\left[\left(-4\right)^2-16^3\right].\left[\left(-4\right)^2-16\right]}{\left(-4\right)^2+16^2+\left(-5\right)^2+1}\)

\(=\frac{\left(-5\right)^5.\left(-4+16^2\right).\left[\left(-4\right)^2-16^3\right].0}{\left(-4\right)^2+16^2+\left(-5\right)^2+1}=0\)

\(\left(x-3\right);\left(y+x\right)\in\left\{-1;1;-7;7\right\}\)

\(\Rightarrow\left(x;y\right)\in\left\{\left(2;-9\right);\left(4;3\right);\left(-4;3\right);\left(10;-9\right)\right\}\left(x,y\in Z\right)\)