不论x为何实数,多项式3x²-5x-1的值总大于2x²-4x-7的值

来源：学生作业帮助网编辑：作业帮时间：2024/05/18 10:31:58

(3x²-5x-1)-(2x²-4x-7)
=3x²-5x-1-2x²+4x+7
=x²-x+6
=(x²-x+1/4)+6-(1/4)
=(x-1/2)²+23/4
∵(x-1/2)²≥0
∴(3x²-5x-1)-(2x²-4x-7)=(x-1/2)²+23/4＞0
即：(3x²-5x-1)-(2x²-4x-7)＞0
∴(3x²-5x-1)＞(2x²-4x-7)
即：不论x为何实数,多项式3x²-5x-1的值总大于2x²-4x-7的值