Prove that x^2 +y^2 +z^2 -xy-yz-zx is always positive.
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They're it's easy
x^3 +y^3+z^3 = x^2+y^2+z^2-xy-yz-zx(x+y+z)
soo you can say that
x^2+y^2+z^2-xy-yz-zx=x^3+y^3+z^3/x+y+z
RHS IS ALWAYS POSITIVE UNLESS
x+y+z = 0
HOPE THIS HELPS U
x^3 +y^3+z^3 = x^2+y^2+z^2-xy-yz-zx(x+y+z)
soo you can say that
x^2+y^2+z^2-xy-yz-zx=x^3+y^3+z^3/x+y+z
RHS IS ALWAYS POSITIVE UNLESS
x+y+z = 0
HOPE THIS HELPS U
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