(a^a)(b^b) + (a^b)(b^a) ≤ 1

 

Let   a   and   b   be positive real numbers such that   a \; + \; b \; = \; 1.

Prove that

a^a \, b^b \; + \; a^b \, b^a \; \leq  \; 1

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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