指數(shù)是b還是b+1啊,沒(méi)寫(xiě)清楚,現(xiàn)在按指數(shù)是b算吧.
a+b=3
b=3-a
2^a+2^b+1
=2^a+2^(3-a)+1
=2^a+8/2^a+1
2^a恒>0
由均值不等式,得2^a=8/2^a時(shí),即a=3/2時(shí),2^a+8/2^a有最小值4√2
此時(shí)2^a+2^b+1有最小值4√2+1