Question

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

Answer 1

Answer:

Step-by-step explajjjnation:

Answer 2

Multiply and divide the whole expression by 2

Then you can break it in the form of

$\frac{{x}^{2} - 2xy + {y}^{2} + {y}^{2} - 2yz + {z}^{2} + {x}^{2} - 2xz + {z}^{2}}{2}$

Now grouping as squares we get

$\frac{{(x - y)}^{2} + {(y - z)}^{2} + {(x - z)}^{2}} {2}$

Now as we know that sum of squares is always positive hence the given expression is always positive

Hope this helps you!!

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