求当x为何值时,代数式6x^2+12x+10/x^2+2x+2可取的最小值,最小值是?

问题描述:

求当x为何值时,代数式6x^2+12x+10/x^2+2x+2可取的最小值,最小值是?

6x^2+12x+10/x^2+2x+2
=6(x^2+2x+2)-2/(x^2+2x+2)
=6-2/(x^2+2x+2)
=6-2/[(x+1)^2+1]
(x+1)^2+1>=1
所以0