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?

来源：学生作业学帮网 编辑：学帮网 时间：2024/05/15 18:23:09

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?

x^2-4x+4y^2-4y+5=0
(x^2-4x+4)+(4y^2-4y+1)=0
(x-2)^2+(2y-1)^2=0
x-2=0
2y-1=0
x=2
y=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

x^2-4x+4y^2-4y+5=0
(x-2)^2+(2y-1)^2=0
x-2=0,x=2
2y-1=0.y=1/2
（x^2+y^2)(x^2-y^2)-(x+y)^2(x-y)^2
=x^4-y^4-(x^2-y^2)^2
=16-1/16-(4-1/4)^2
=255/16-9/16
=246/16
=123/8

两式子化简得 X^2-4x+4+4y^2-4y+1=0
即：（x-2)^2+(2y-1)^2=0

可以看出：（x-2)^2=0 （2y-1)^2=0
x=2 y=1/2
再将后面式子化简 把x y 值代入即可

由x^2-4x+4y^2-4y+5=0得
（x-2)^2+(2y-1)^2=0
所以x=2，y=1/2;
代入（x^2+y^2)(x^2-y^2)-(x+y)^2(x-y)^2得
原式=15/8;

x^2-4x+4y^2-4y+5=0可化简为
(x-2)^2+(2y-1)^2=0
得：x=2
y=1/2
（x^2+y^2)(x^2-y^2)-(x+y)^2(x-y)^2
=2x^2y^2-2y^4
=2y^2(x^2-y^2)
代入x及y的值得
2*(1/2)^2[2^2-(1/2)^2]=15/8

已知x*x+4x+y*y-2y+5=0,则x*x+y*y=? 已知X.x+y.y-4x+2y+5=0,求4X.X-12X Y+9Y.y的值 已知x*x-4xy+4y*y=0 求[2x(x+y)-y(x+y)]/(4x*x-4xy+y*y)的值? 已知4x^2+y^2-4x+4y+5=0,求x,y 已知x-y+2>=0,x+y-4>=4,2x-y-5 已知{x-y+2>=0,x+y-4>=0,2x-y-5 已知x^2+y^2-4x+2y+5=0则x^y=? 已知x^2+4x+y^2+2y+5=0,则x^y= 已知x²+4x+y-2y+5=0求x+2y 已知x²+4x+y²-2y+5=0,则x+y= 已知x²+y²-2x+4y+5=0,求x+y 已知|5x-y-8|+(7y-x+2)=0则4x+6y 已知x,y>0 2x+y+3=xy 求5x+4y最小值 已知X^2+Y^2-2X-4Y+5=0,求分式Y/X-X/Y的值 已知x²+y²-2x-4y+5=0,求分式y/x-x/y的值. 已知x、y满足x²+y²+2x-4y+5=0,求x、y的值 已知x²+4y²-4x+4y+5=0,求：(x^4-y^4)/[(2x-y)(x+y)]*(2x-y)/(xy-y²)/[(x²+y²)²/y²] 已知x²+4y²-4x+4y+5=0,求(2x-y)(x+y)/x四次方-y四次方×xy-y²/2x-y÷(y/x²+y²)²