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Is there a neat proof for a simple looking inequality.good reason why a^{2b} + b^{2a} <= 1 when a+b=1? |
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A Is there a neat proof for a simple looking inequality. |
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The following problem is not from me, yet I find it a big challenge to give a nice (in contrast to 'heavy computation') proof. The motivation for me to post it lies in its concise content. If $a$ and $b$ are nonnegative real numbers such that $a+b=1$, then show that $a^{2b} + b^{2a}\le 1$. |
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