求证题(有关一元二次的)
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求证题(有关一元二次的)
求证:不论x为何实数,多项式3x^2-5x-1的值大于2x^2-4x-7的值
求证:不论x为何实数,多项式3x^2-5x-1的值大于2x^2-4x-7的值
![求证题(有关一元二次的)](/uploads/image/z/18780591-39-1.jpg?t=%E6%B1%82%E8%AF%81%E9%A2%98%EF%BC%88%E6%9C%89%E5%85%B3%E4%B8%80%E5%85%83%E4%BA%8C%E6%AC%A1%E7%9A%84%EF%BC%89)
(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
(x-1/2)^2≥0
所以(x-1/2)^2+23/4>0
所以(3x^2-5x-1)-(2x^2-4x-7)>0
所以不论x为何实数
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
(x-1/2)^2≥0
所以(x-1/2)^2+23/4>0
所以(3x^2-5x-1)-(2x^2-4x-7)>0
所以不论x为何实数
3x^2-5x-1>2x^2-4x-7