Unformatted text preview: x,y,z and w . Use this inequality to prove that a 3 + b 3 + c 3 ≥ 3 abc for any real nonnegative numbers a,b,c . (Hint: For the ﬁrst part, use the Arithmetic MeanGeometric Mean inequality for two numbers. For the second part, make w := 3 √ xyz in the ﬁrst inequality.) 6. Bonus Question! Prove that: x 2 + y 2 + z 2 ≥ xy + yz + zx. for any real numbers x,y and z , When does equality hold ?...
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 Fall '10
 CIOABA
 Real Numbers, Sets, Negative and nonnegative numbers, meangeometric mean inequality

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