Question

Tìm x và y, z, biết 

 X^2+5y^2-4xy+10x-22y+|x+y+z|+26=0

Em cảm ơn ạ

Answer 1

\(x^2+5y^2-4xy+10x-22y+\left|x+y+z\right|+26=0\)

\(\Leftrightarrow\left[x^2-2x\left(2y-5\right)+\left(2y-5\right)^2\right]+\left(y^2-2y+1\right)+\left|x+y+z\right|=0\)

\(\Leftrightarrow\left(x-2y+5\right)^2+\left(y-1\right)^2+\left|x+y+z\right|=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-2y+5=0\\y-1=0\\x+y+z=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=-3\\y=1\\z=2\end{matrix}\right.\)