高校问答何韵诗是何鸿燊女儿吗:求解等式
来源：百度文库 编辑：高校问答 时间：2024/04/20 02:44:38
计算(x+y+z)(-x+y+z)(x-y+z)(x+y-z)
谢谢，怎么解？？
谢谢，怎么解？？
(x+y+z)(-x+y+z)(x-y+z)(x+y-z)
=[(x+y+z)(x+y-z)]*{[z+(x-y)][z-(x-y)]}
=[(x+y)^2-z^2][z^2-(x-y)^2]
=(x^2+2xy+y^2-z^2)[z^2-(x-y)^2]
=4*x^2*y^2-(x^2+y^2-z^2)^2
另外免费赠送一道我做过的数学题，仅供参考
已知x2+y2=z2,xy=1,求(x+y+z)(x-y+z)(-x+y+z)(x+y-z)的值。
解：(x+y+z)(x-y+z)(-x+y+z)(x+y-z)
=(x2+2xy+y2-z2)[z2-(x-y)2]
=2(z2-x2+2xy-y2)
=4xy =4