Question

Prove that x^2+y^2+z^2+-xy-yz-zx is always positive.
Please answer as fast as you can.​

Answer 1

Step-by-step explanation:

X2+y2+z2-xy-yz-zx<0 (let)

=> 2(X2+y2+z2-xy-yz-zx)<0

=> x2+y2-2xy+y2+z2-2yz+z2+x2-2xz <0

=> (x-y)2+(y-z)2+(z-x)2 <0

Which is not true since sum of squares is always greater than 0.

Hence proved