函数y=(x²+8)/(x-1) (x＞1)的最小值是

题目

函数y=(x²+8)/(x-1) (x＞1)的最小值是
函数y=(x²+8)/(x-1) (x＞1)的最小值是

答案

x>1即x-1>0
y=(x²-1)/(x-1)+9/(x-1)
=x+1+9/(x-1)
=(x-1)+9/(x-1)+2≥2√[(x-1)*9/(x-1)]+2=8
所以最小值是8