求分式y=3x^2+6x+5/x^2+2x+2的取值范围
问题描述:
求分式y=3x^2+6x+5/x^2+2x+2的取值范围
答
3x^2+6x+5 = 3(x^2+2x+2) -1
所以 y = 3x^2+6x+5/x^2+2x+2 = 3 - 1/(x^2+2x+2)
因为 x^2+2x+2 = (x+1)^2 +1 >=1,
所以 0