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Let a and b be positive real numbers such that a+b =1. Prove that a^a b^b + a^bb^a ≤ 1.

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Let a and b be positive real numbers such that a+b =1. Prove that aa bb + abba ≤ 1.

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Observe

1 = a + b = aa + bba + b = aabb + babb.

Hence

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