Question

Cho x,y,z,>0. Tìm GTNN

\(G=\frac{x}{y}+\frac{y}{z}+\frac{z}{x}\)

Answer 1

Áp dụng BĐT AM-GM ta có:

\(G\ge3.\sqrt[3]{\frac{x}{y}.\frac{y}{z}.\frac{z}{x}}=3.\sqrt[1]{3}\)

Dấu " = " xảy ra <=> \(\frac{x}{y}=\frac{y}{z}=\frac{z}{x}\Leftrightarrow x=y=z\)