theo bat dang thuc C-S ta co
\(P\le\frac{x}{x+\sqrt{xy}+\sqrt{xz}}+\frac{y}{y+\sqrt{yz}+\sqrt{yx}}+\frac{z}{z+\sqrt{zx}+\sqrt{zy}}\)
\(=\frac{\sqrt{x}}{\sqrt{x}+\sqrt{y}+\sqrt{z}}+\frac{\sqrt{y}}{\sqrt{x}+\sqrt{y}+\sqrt{z}}+\frac{\sqrt{z}}{\sqrt{x}+\sqrt{y}+\sqrt{z}}=1\)
Vay GTLN cua P la 1 dau = khi x=y=z