4 Made the title an actual question

3 Title

# AIsthereaneatprooffora simple looking inequality.

2 added 5 characters in body

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 $a^{2b} + b^{2a}\le 1$.

1