已知 x+y=4,x^2+y^2=10 求x-y的值

(x+y)^2=16,因为x^2+y^2=10 ，所以2xy=6
x^2-2xy+y^2=(x-y)^2=4,所以x-y=2或-2

(x+y)^2=x^2+y^2+2xy
则xy=3
又由x+y=4得
(x=1,y=3)或(x=3,y=1)
故x-y=-2或2

(x+y)^2=16
x^2+2xy+y^2=16 (1)
x^2+y^2=10 (2)
(1)-(2)=2xy=6 (3)
(2)-(3)=x^2+y^2-2xy=4=(x-y)^2=4
x-y=-2或2

因为(x+y)^2=16,
即x^2+2xy+y^2=16
且x^2+y^2=10 ，
所以
x^2+2xy+y^2-(x^2+y^2)
2xy=6
x^2-2xy+y^2
=(x-y)^2
=4,
所以x-y=2或-2