数学题(x+y+z-2)^2+(y+z+2-x)^2急求!

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数学题(x+y+z-2)^2+(y+z+2-x)^2急求!

数学题(x+y+z-2)^2+(y+z+2-x)^2急求!
数学题(x+y+z-2)^2+(y+z+2-x)^2急求!

数学题(x+y+z-2)^2+(y+z+2-x)^2急求!
答:
(x+y+z-2)^2+(y+z+2-x)^2
=(x+y+z-2+y+z+2-x)^2-2(x+y+z-2)(y+z+2-x)
=(2y+2z)^2-2*[(y+z)^2-(2-x)^2]
=4(y+z)^2-2(y+z)^2+2(x-2)^2
=2(y+z)^2+2(x-2)^2

(x+y+z-2)^2+(y+z+2-x)^2
=[(y+z)+(x-2)]^2+[(y+z)-(x-2)]^2
=[(y+z)^2+2(y+z)(x-2)+(x-2)^2]+[(y+z)^2-2(y+z)(x-2)+(x-2)^2]
=2(y+z)^2+2(x-2)^2
=2(y^2+2yz+z^2)+2(x^2-4x+4)
=2y^2+4yz+2z^2+2x^2-8x+8

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