不论x为何实数,多项式3x²-5x-1的值总大于2x²-4x-7的值
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![不论x为何实数,多项式3x²-5x-1的值总大于2x²-4x-7的值](/uploads/image/z/1614974-14-4.jpg?t=%E4%B8%8D%E8%AE%BAx%E4%B8%BA%E4%BD%95%E5%AE%9E%E6%95%B0%2C%E5%A4%9A%E9%A1%B9%E5%BC%8F3x%26%23178%3B-5x-1%E7%9A%84%E5%80%BC%E6%80%BB%E5%A4%A7%E4%BA%8E2x%26%23178%3B-4x-7%E7%9A%84%E5%80%BC)
不论x为何实数,多项式3x²-5x-1的值总大于2x²-4x-7的值
不论x为何实数,多项式3x²-5x-1的值总大于2x²-4x-7的值
不论x为何实数,多项式3x²-5x-1的值总大于2x²-4x-7的值
(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