已知x2+y2+4x-8y+20=0先化简再求值(x-y)2(x+y)2-(x2+y2)2

已知x2+y2+4x-8y+20=0先化简再求值(x-y)2(x+y)2-(x2+y2)2
已知x2+y2+4x-8y+20=0先化简再求值
(x-y)2(x+y)2-(x2+y2)2

已知x2+y2+4x-8y+20=0先化简再求值(x-y)2(x+y)2-(x2+y2)2
x2+y2+4x-8y+20=0
(x+2)^2+(y-4)^2=0
所以x=-2 y=4
(x-y)2(x+y)2-(x2+y2)2
=(x^2-y^2)^2-(x^2+y^2)^2
=2x^2*(-2y^2)
=-4*(xy)^2
=-4*(-8)^2
=-256

x^2+y^2+4x-8y+20=0
(x+2)^2+(y-4)^2=0
x=-2,y=4
(x-y)2(x+y)2-(x2+y2)2
=(-2-4)^2*(-2+4)^2-(4+16)^2
=36*4-400
=-256

晕哦，这个典型的配方啊，把已知式化成：（X+2)²+（Y-4）²=0，∴X=-2,Y=4，剩下的就自己解决了

原式=x2+4x+4+y2-8y+16=0=(x+2)2+(y-4)2=0
x=-2 y=+4
将x=-2 y=+4带入(x-y)2(x+y)2-(x2+y2)2
(x-y)2(x+y)2-(x2+y2)2=（-2-4）2（-2+4）2-(4+16)2
=36*4-400
=144-400
=256