已知x^2+y^2=10,xy=3,求x-y

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已知x^2+y^2=10,xy=3,求x-y已知x^2+y^2=10,xy=3,求x-y已知x^2+y^2=10,xy=3,求x-yx^2+y^2=10(x-y)^2+2xy=10(x-y)^2=4x

已知x^2+y^2=10,xy=3,求x-y
已知x^2+y^2=10,xy=3,求x-y

已知x^2+y^2=10,xy=3,求x-y
x^2+y^2=10
(x-y)^2+2xy=10
(x-y)^2=4
x-y=±2

(x-y)^2=x^2+y^2-2xy
所以（x-y)^=10-6=4
所以 x-y=2

(x-y）^2=x^-2xy+y^2=10-6=4 ∴x-y=正负2

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