Question

[Trần Ngọc Tú]

Cho \(\frac{x^2}{y+z}+\frac{y^2}{z+x}+\frac{z^2}{z+x}=\)0 ( x + y + z \(\ne\)0 )

CMR : \(\frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y}=1\)

Answer 1

[Nguyễn Linh Chi]

Ta có

\(x+y+z+\frac{x^2}{y+z}+\frac{y^2}{z+x}+\frac{z^2}{y+x}=x+y+z\)

=> \(x+\frac{x^2}{y+z}+y+\frac{y^2}{z+x}+z+\frac{z^2}{y+x}=x+y+z\)

=> \(\frac{x\left(x+y+z\right)}{y+z}+\frac{y\left(x+y+z\right)}{z+x}+\frac{z\left(x+y+z\right)}{y+x}=x+y+z\)

=> \(\frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{y+x}=1\)