均值不等式解函数

问题描述:

均值不等式解函数
f(x)=(x²-x=1)/(x-1) (x>1)
f(x)=(x²-x+1)/(x-1) (x>1) 打错了

f(x)=(x²-x)/(x-1)+1/(x-1)
=x+1/(x-1)
=(x-1)+1/(x-1)+1
x>1,x-1>0
所以f(x)≥2√[(x-1)*1/(x-1)]+1=2+1=3
最小值是3x>1,x-1>0所以f(x)≥2√[(x-1)*1/(x-1)]+1=2+1=3最小值是3这里没看懂a+b>=2√ab