用換元法,取m = x^2 - 4
則x^2 = m+4
所以y = x^2 + 1/(x^2 - 4)
= m + 4 + 1/m
= (m + 1/m) + 4
>= 2 + 4 = 6
當(dāng)且僅當(dāng)m = 1/m時(shí)取等號(hào)
此時(shí)m^2 = 1,即x^2 - 4 = 1
因?yàn)閤 > 2,所以此時(shí)x = 根號(hào)5
即,x=根號(hào)5時(shí)y有最小值6.