Question

[Alice Sophia]

Cho P=x/(y+z)+y/(z+x)+z/(x+y);Q=x²/(y+z)+y²/(z+x)+z²/(x+y)

Cm P=1 thì Q=0

Answer 1

[Đinh Đức Hùng]

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

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

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

\(\Rightarrow Q=\frac{x^2}{y+z}+\frac{y^2}{x+y}+\frac{z^2}{x+y}=0\) (dpcm)