Question

Cho x ,y ,z thỏa mãn : x+ y+z =0 . Chứng minh rằng : xy+2yz+3zx ≤ 0

Answer 1

\(xy+2yz+3zx=xy+zx+2yz+2zx=x\left(y+z\right)+2z\left(y+x\right)=x.\left(-x\right)+2z.\left(-z\right)=-x^2-2z^2\le0\)-Dấu bằng xảy ra \(\Leftrightarrow x=y=z=0\)