SOLUTION: prove that for x,y,z>=0, x^2+y^2+z^2>=xy+yz+zx

SOLUTION: prove that for x,y,z>=0, x^2+y^2+z^2>=xy+yz+zx

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Question 461593: prove that for x,y,z>=0, x^2+y^2+z^2>=xy+yz+zx
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Consider the vectors (x, y, z) and ( , ,).
Then direct application of the Cauchy-Schwartz Inequality gives:

.
we don't even need the non-negativity conditions for x, y, and z.
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