2的y次方+2的x次方=6,则2的x+y次方的最大值

题目

2的y次方+2的x次方=6,则2的x+y次方的最大值

答案

2^y+2^x=6
6=2^y+2^x≥2√[2^(x+y)]
3≥√[2^(x+y)]
2^(x+y)]≤9
(2^(x+y)])(MAX)=9