Question

Tìm x,y,z biết : x²+y²+z²=y(x+z)

Answer 1

Ta có:

\(x^2+y^2+z^2=y\left(x+z\right)\\ \Leftrightarrow x^2+y^2+z^2-yx-yz=0\\ \Leftrightarrow2x^2+2y^2+2z^2-2yx-2yz=0\\ \Leftrightarrow\left(x-y\right)^2+\left(y-z\right)^2+x^2+z^2=0\\ \Leftrightarrow\left\{{}\begin{matrix}x-y=0\\y-z=0\\x=0\\z=0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=y\\y=z\\x=0\\z=0\end{matrix}\right.\\ \Leftrightarrow x=y=z=0\)

Đúng thì tích"Đúng" mk với bạn nhé!