证明：不论x为何实数,多项式3x²-5x-1的值总大于2x²-4x-7的值.
问题描述：
证明：不论x为何实数,多项式3x²-5x-1的值总大于2x²-4x-7的值.
答
两式想减得:
x^2 - x + 6
= (x-1/2)^2 + 6 - 1/4
>0
答
两个式子相减
3x^2-5x-1-(2x^2-4x-7)
=3x^2-5x-1-2x^2+4x+7
=x^2-x+6
=(x^2-x+1/4)+23/4
=(x-1/2)^2+23/4>0
所以3x²-5x-1>2x²-4x-7