已知x^2-xy=60´xy-y^2=40,求代数式x^2-y^2和x^2.-2xy+y^2的值

已知x^2-xy=60´xy-y^2=40,求代数式x^2-y^2和x^2.-2xy+y^2的值
已知x^2-xy=60´xy-y^2=40,求代数式x^2-y^2和x^2.-2xy+y^2的值

已知x^2-xy=60´xy-y^2=40,求代数式x^2-y^2和x^2.-2xy+y^2的值
∵x²-xy=60;xy-y²=40.
x(x-y)=60;y(x-y)=40
x-y=60/x; y*60/x=40
y/x=2/3
y=2/3x;x=3/2y
x²-xy=60
x²-2/3x²=60
1/3x²=60
x²=180
xy-y²=40
3/2y²-y²=40
1/2y²=40
y²=80
x²-y²=180-80=100
x²-2xy+y²=(x-y)²=(60/x)²=360/x²=360/180=2