试说明(2-x)(x-3)(x^2-5x-14)≤100 急求啊！！！！！！！！！！！！！！！！！！！！！！！！！！！！！
答案:6 悬赏:0 手机版
解决时间 2021-03-08 09:45
- 提问者网友：几叶到寒
- 2021-03-08 03:05
试说明(2-x)(x-3)(x^2-5x-14)≤100 急求啊！！！！！！！！！！！！！！！！！！！！！！！！！！！！！
最佳答案
- 五星知识达人网友：青尢
- 2021-03-08 03:47
(2-x)(x-3)(x^2-5x-14)-100
= - (x-2)(x-3)(x^2-5x-14)+100
=-（x^2-5x+6）(x^2-5x-14)+100
=-(x^2-5x）^2+(6-14)*(x^2-5x)-6*14+100
=-(x^2-5x）^2-8*(x^2-5x)+16
=-(x^2-5x）^2-8*(x^2-5x)+4^2
=-(x^2-5x-4)^2≤0追问已知长方形的长为x，宽为y，周长为16，面积为15，求x^3 y+2x^2y^2+xy^3的值追答2*(x+y)=16 即 x+y=8
x*y=15
x^3 y+2x^2y^2+xy^3
=x*y*(x^2+2*x*y+y^2)
=x*y*(x+y)^2
=15*8^2
=15*64
=960
还可以知道x=5 y=3
= - (x-2)(x-3)(x^2-5x-14)+100
=-（x^2-5x+6）(x^2-5x-14)+100
=-(x^2-5x）^2+(6-14)*(x^2-5x)-6*14+100
=-(x^2-5x）^2-8*(x^2-5x)+16
=-(x^2-5x）^2-8*(x^2-5x)+4^2
=-(x^2-5x-4)^2≤0追问已知长方形的长为x，宽为y，周长为16，面积为15，求x^3 y+2x^2y^2+xy^3的值追答2*(x+y)=16 即 x+y=8
x*y=15
x^3 y+2x^2y^2+xy^3
=x*y*(x^2+2*x*y+y^2)
=x*y*(x+y)^2
=15*8^2
=15*64
=960
还可以知道x=5 y=3
全部回答
- 1楼网友：低音帝王
- 2021-03-08 08:31
(2-x)(x-3)(x^2-5x-14)-100
= - (x-2)(x-3)(x^2-5x-14)+100
=-（x^2-5x+6）(x^2-5x-14)+100
=-(x^2-5x）^2+(6-14)*(x^2-5x)-6*14+100
=-(x^2-5x）^2-8*(x^2-5x)+16
=-(x^2-5x）^2-8*(x^2-5x)+4^2
=-(x^2-5x-4)^2≤0
= - (x-2)(x-3)(x^2-5x-14)+100
=-（x^2-5x+6）(x^2-5x-14)+100
=-(x^2-5x）^2+(6-14)*(x^2-5x)-6*14+100
=-(x^2-5x）^2-8*(x^2-5x)+16
=-(x^2-5x）^2-8*(x^2-5x)+4^2
=-(x^2-5x-4)^2≤0
- 2楼网友：酒者煙囻
- 2021-03-08 07:36
(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
=-(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
- 3楼网友：雾月
- 2021-03-08 06:24
∵(2-x)(x-3)(x^2-5x-14)-100
= - (x-2)(x-3)(x^2-5x-14)+100
=-（x^2-5x+6）(x^2-5x-14)+100
=-(x^2-5x）^2+(6-14)*(x^2-5x)-6*14+100
=-(x^2-5x）^2-8*(x^2-5x)+16
=-(x^2-5x）^2-8*(x^2-5x)+4^2
=-(x^2-5x-4)^2≤0
∴(2-x)(x-3)(x^2-5x-14)≤100
= - (x-2)(x-3)(x^2-5x-14)+100
=-（x^2-5x+6）(x^2-5x-14)+100
=-(x^2-5x）^2+(6-14)*(x^2-5x)-6*14+100
=-(x^2-5x）^2-8*(x^2-5x)+16
=-(x^2-5x）^2-8*(x^2-5x)+4^2
=-(x^2-5x-4)^2≤0
∴(2-x)(x-3)(x^2-5x-14)≤100
- 4楼网友：一袍清酒付
- 2021-03-08 05:25
(2-x)(x-3)(x^2-5x-14)-100
= - (x-2)(x-3)(x^2-5x-14)+100
=-（x^2-5x+6）(x^2-5x-14)+100
=-(x^2-5x）^2+(6-14)*(x^2-5x)-6*14+100
=-(x^2-5x）^2-8*(x^2-5x)+16
=-(x^2-5x）^2-8*(x^2-5x)+4^2
=-(x^2-5x-4)^2<=0
= - (x-2)(x-3)(x^2-5x-14)+100
=-（x^2-5x+6）(x^2-5x-14)+100
=-(x^2-5x）^2+(6-14)*(x^2-5x)-6*14+100
=-(x^2-5x）^2-8*(x^2-5x)+16
=-(x^2-5x）^2-8*(x^2-5x)+4^2
=-(x^2-5x-4)^2<=0
- 5楼网友：思契十里
- 2021-03-08 05:13
可以适当的进行代换设定，让代数式看起来简洁些~过程如图
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