10. Prove that :x2 + y2 + z2 - xy - yz - zx is always positive. – InterviewSolution

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10. Prove that :x2 + y2 + z2 - xy - yz - zx is always positive.

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x²+y²+z²-xy-yz-zx

=1/2[2x²+2y²+2z²–2xy-2yz-2zx]

=(1/2)[(x²+y²–2xy(+(y²+z²–2yz)+(z²+x²–2zx)]

=(1/2)[(x-y)²+(y-z)²+(z-x)²]

=Always positive since ( All squres are +ve)

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