若a>1,则a+(1/a-1)的最小值a加上1/a-1

Question

若a>1,则a+ (1/a-1)的最小值
a 加上 1/a-1

Answer 1

a-1都在分母吧?
∵a＞1
∴a-1＞0
a + [1/(a-1)]
= a-1 + [1/(a-1)] + 1
≥2√[(a-1)×1/(a-1)] + 1
=3
当且仅当a-1 = 1/(a-1) , 即a = 2时,取等号