已知：x-y+1=0,xy-2x-2y-7=0,求x2+y2以及4x2y2-x4-y4.

已知：x-y+1=0,xy-2x-2y-7=0,求x2+y2以及4x2y2-x4-y4.
已知：x-y+1=0,xy-2x-2y-7=0,求x2+y2以及4x2y2-x4-y4.

已知：x-y+1=0,xy-2x-2y-7=0,求x2+y2以及4x2y2-x4-y4.
x-y+1=0
y=x+1
代入xy-2x-2y-7=0
得x(x+1)-2x-2(x+1)-7=0
x1=(3+3√5)/2,x2=(3-3√5)/2
y1=(5+3√5)/2,y2=(5-3√5)/2
x^2+y^2=31+12√5
或31-12√5
4x2y2-x4-y4=-(x^2-y^2)^2
-(x^2-y^2)^2=-61+24√5
或-61-24√5

已知x-y+1=0(1)
xy-2x-2y-7=0(2)
x=y-1
则y(y-1)-2(y-1)-2y-7=0
y^2-y-2y+2-2y-7=0
y^2-4y-5=0
(y+1)(y-5)=0
所以1.y=-1 则x=-2 那么x^2+y^2=5, 4x^2y^2-x^4-y^4=-1
2.当y=5时 则x=4 那么x^2+y^2=41， 4x^2y^2-x^4-y^4=719