试说明(2-x)(x-3)(xx-5x-14)小于等于100

题目

试说明(2-x)(x-3)(xx-5x-14)小于等于100

答案

(2-x)(x-3)(xx-5x-14)
=-(x^2-5x+6)(x^2-5x-14)
=-(x^2-5x)^2+8(x^2-5x)^+84
=100-(x^2-5x-4)^2
≤100
所以(2-x)(x-3)(xx-5x-14)小于等于100