1／2（x+y+z）²＋1／2（x－y－z)(x－y＋z)－z(x＋y),其中x-y=6，xy=21
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解决时间 2021-05-12 02:33
- 提问者网友：椧運幽默
- 2021-05-11 03:55
最佳答案
- 五星知识达人网友：轻雾山林
- 2021-05-11 05:01
1/2(x+y+z)^2+1/2[(x-y)^2-2z(x-y)+z^2]-z(x+y)
=1/2(x+y)^2+z(x+y)+1/2*z^2+1/2(x-y)^2-z(x-y)+1/2*z^2-z(x+y)
=1/2(x+y)^2+1/2(x-y)^2+z^2-z(x-y)
=1/2(x^2-2xy+y^2+4xy)+1/2(x-y)^2+z^2-z(x-y)
=1/2(x-y)^2+2xy+1/2(x-y)^2+z^2-z(x-y)
=(x-y)^2+2xy-z(x-y)+z^2
代入，x-y=6,xy=21
原式=6^2+2*21-6z+z^2
=36+42-6z+z^2
=78-6z+z^2
=1/2(x+y)^2+z(x+y)+1/2*z^2+1/2(x-y)^2-z(x-y)+1/2*z^2-z(x+y)
=1/2(x+y)^2+1/2(x-y)^2+z^2-z(x-y)
=1/2(x^2-2xy+y^2+4xy)+1/2(x-y)^2+z^2-z(x-y)
=1/2(x-y)^2+2xy+1/2(x-y)^2+z^2-z(x-y)
=(x-y)^2+2xy-z(x-y)+z^2
代入，x-y=6,xy=21
原式=6^2+2*21-6z+z^2
=36+42-6z+z^2
=78-6z+z^2
全部回答
- 1楼网友：时间的尘埃
- 2021-05-11 07:52
没有z的关系？怎么求呢？
- 2楼网友：持酒劝斜阳
- 2021-05-11 06:29
化简下来就是X²+Y²=78
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