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March 30th, 2014, 11:46 AM   #1
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Inequality challenge

Given some real numbers with
prove that
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March 31st, 2014, 08:41 AM   #2
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Hint:
Consider the polynomial
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March 31st, 2014, 10:03 AM   #3
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It's easy to show that (4/3)x³ + 1/3 ≥ x for x ≥ -1.
Applying that to each numbered x variable and adding gives the desired inequality.
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March 31st, 2014, 10:38 AM   #4
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Well done!
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