Để ý: \(2=\left(\frac{x}{y}+\frac{y}{z}\right)+\left(\frac{y}{z}+\frac{z}{x}\right)+\left(\frac{z}{x}+\frac{x}{y}\right)\)
\(\ge2\sqrt{\frac{x}{z}}+2\sqrt{\frac{y}{x}}+2\sqrt{\frac{z}{y}}\)
Từ đó suy ra \(\sqrt{\frac{y}{x}}+\sqrt{\frac{z}{y}}+\sqrt{\frac{x}{z}}\le1\)