Question

若x-y=6,xy=-8,求代数式(x+y+z)²+(x-y-z)(x-y+z)-2·z(x+y)的值

Answer 1

您好：

(x+y+z)²+(x-y-z)(x-y+z)-2·z(x+y)
=(x+y)²+2z(x+y)+z²+(x-y)²-z²-2z(x+y)
=(x+y)²+(x-y)²
=(x-y)²+4xy+6²
=6²-4x8+36
=72-32
=40

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Answer 2

x+y=+/-2，xy=-8，x-y=6
原式=(2+/-z)^2+(6-z)(6+z)-/+4z
(1) x+y=2，原式=(2+z)^2+36-z^2-4z=40
(2)x+y=-2，原式=(2-z)^2+36-z^2+4z=40
故(x+y+z)²+(x-y-z)(x-y+z)-2·z(x+y)=40