Question

Prove that :
x^2 + y^2 + z^2 - xy - yz – zx is always positive.

Answer 1

ANSWER

CONCEPT USED

(X-Y) ^2 = X^2+Y^2-2XY

PROOF

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Answer 2

Answer:

x^2+y^2+z^2-xy-yz-zx

1/2(2x^2+2y^2+2z^2-2xy-2yz-2zx)

1/2( (x^2-2xy+y^2)+(y^2-2yz+z^2)+(x^2-2xz+z^2))

1/2((x-y)^2+(y-z)^2+(x-z)^2)

which is zero(0) if x=y=z

in all other cases,it is positive

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