已知正实数a,b满足1⼀a+2⼀b =3,则(a+1)(b+2)的最小值是? 求详解

2025-01-24 05:31:32
推荐回答(1个)
回答1:

1/a+2/b =3
(2a+b)/ab=3
2a+b=3ab
3ab=2a+b≥2根号(2ab)
ab≥8/9
(a+1)(b+2)
=ab+2a+b+2
=4ab+2
≥32/9+2=50/9
所以
(a+1)(b+2)的最小值是50/9