比较下列一组中两个代数式大小(x²+y²)(x-y)与(x²-y²)(x+y)(x>y>0)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 19:35:04
![比较下列一组中两个代数式大小(x²+y²)(x-y)与(x²-y²)(x+y)(x>y>0)](/uploads/image/z/7648249-49-9.jpg?t=%E6%AF%94%E8%BE%83%E4%B8%8B%E5%88%97%E4%B8%80%E7%BB%84%E4%B8%AD%E4%B8%A4%E4%B8%AA%E4%BB%A3%E6%95%B0%E5%BC%8F%E5%A4%A7%E5%B0%8F%28x%26%23178%3B%2By%26%23178%3B%29%28x-y%29%E4%B8%8E%28x%26%23178%3B-y%26%23178%3B%29%28x%2By%29%EF%BC%88x%EF%BC%9Ey%EF%BC%9E0%EF%BC%89)
比较下列一组中两个代数式大小(x²+y²)(x-y)与(x²-y²)(x+y)(x>y>0)
比较下列一组中两个代数式大小
(x²+y²)(x-y)与(x²-y²)(x+y)(x>y>0)
比较下列一组中两个代数式大小(x²+y²)(x-y)与(x²-y²)(x+y)(x>y>0)
解(x²+y²)(x-y)-(x-y)(x+y)(x+y)
=(x-y)【(x²+y²)-(x+y)(x+y)】
=(x-y)【(x²+y²)-x²-y²-2xy】
=(x-y)【-2xy】
由x>y>0
即x-y>0,-2xy<0
即
(x-y)【-2xy】<0
即x²+y²)(x-y)<(x²-y²)(x+y)
S
<