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)
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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.
