Question

Buna, imi puteti da un hint cum as putea demonstra asta:
$x^{2} +y^{2} + z^{2} \geq x * y + x * z + y * z$

Answer 1

2x²+2y²+2z²≥2xy+2yz+2zx

2x²+2y²+2z²-2xy-2yx-2zx≥0

x²-2xy+y²+y²-2yz+z²+z²-2zx+x²≥0

(x-y)²+(y-z)²+(z-x)²≥0