已知x^2-4x+4y^2-4y+5=0,求（x^2+y^2)(x^2-y^2)-(x+y)^2(x-y)^2的值?
问题描述：
已知x^2-4x+4y^2-4y+5=0,求（x^2+y^2)(x^2-y^2)-(x+y)^2(x-y)^2的值?
答
x^2-4x+4y^2-4y+5=0(x^2-4x+4)+(4y^2-4y+1)=0(x-2)^2+(2y-1)^2=0x-2=02y-1=0x=2y=1/2原式=x^4-y^4-[(x+y)(x-y)]^2=x^4-y^4-(x^2-y^2)^2=x^4-y^4-x^4+2x^2y^2-y^4=2x^2y^2-2y^4=2*4*1/4-2*1/16=15/8