函数y=x²+2/x-1(x>1)的最小值是

题目

函数y=x²+2/x-1(x>1)的最小值是
答案是2根号3+2求解

答案

解
y=x^2+2/x-1
=[(x-1)^2+2x+1]/(x-1)
=[(x-1)^2+2（x-1）+3]/(x-1)
=（x-1）+3/(x-1)+2
≥2√（x-1）×3/(x-1) +2
=2√3 +2