Question

求教大学中值定理证明：2倍根号x大于3-(1/x) (x大于0)

Answer 1

2√x>3-1/x

√x+√x+1/x>3

根据中值定理(a+b+c)/3>=(abc)^(1/3)

则√x+√x+1/x>=3(√x*√x*1/x)^(1/3)=3

当x=1时等号成立.