来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/11/12 15:38:31
初二一道数学题不会~~~~
(x²-4)×(x²-10x+21)+100证明此的值为非负数
(x²-4)×(x²-10x+21)+100
= (x+2)(x-2)(x-3)(x-7)+100
= (x^2 - 4)((x-5)^2 - 4) + 100
= x^2(x-5)^2 - 4(x^2+(x-5)^2) + 16 + 100
= (x(x-5))^2 - 4(2x^2-10x)-100+16+100
= (x(x-5))^2 - 8x(x-5)+16
= (x(x-5) - 4)^2
>= 0