Folosim inegalitatea mediilor:
[tex]m_a\geq m_g[/tex]
[tex]\frac{x^2+y^2}{2}\geq \sqrt{x^2y^2}\rightarrow \frac{x^2+y^2}{2}\geq xy\\
\frac{x^2+z^2}{2}\geq \sqrt{x^2z^2}\rightarrow \frac{x^2+z^2}{2}\geq xz\\
\frac{y^2+z^2}{2}\geq \sqrt{y^2z^2}\rightarrow \frac{y^2+z^2}{2}\geq yz\\
\rule{200}{0.5}+\\
\frac{2x^2+2y^2+2z^2}{2}\geq xy+xz+yz\\
\boxed{x^2+y^2+z^2\geq xy+xz+yz}
[/tex]
