Question

用不等式解决问题：已知正数a.b满足a+b=1求证ab+1/ab>=17/4

Answer 1

1=a+b≥2√ab
所以ab≤1/4
所以1/ab≥4
ab+1/ab
=ab+1/16ab+15/16ab≥2√(ab*1/16ab)+15/16ab≥1/2+(15/16)*4=17/4
即
ab+1/ab≥17/4