Folosim inegalitatea dintre media aritmetica si media geometrica.
[tex] \frac{x+y}{2} \geq \sqrt{x\cdot y} =>x+y\geq2\sqrt{x \cdot y}\\
\frac{y+z}{2} \geq \sqrt{y\cdot z} =>y+z\geq2\sqrt{y \cdot z}\\
\frac{z+x}{2} \geq \sqrt{z\cdot x} =>z+x\geq2\sqrt{z \cdot x}\\
(x+y)(y+z)(z+x)\geq8\sqrt{x^2\cdot y^2 \cdot z^2}\\
(x+y)(y+z)(z+x)\geq8\cdot x\cdot y \cdot z[/tex]
