如果x+y=3,x^2+y^2=6,x^4-y^4=24,那么x-y=?

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如果x+y=3,x^2+y^2=6,x^4-y^4=24,那么x-y=?

如果x+y=3,x^2+y^2=6,x^4-y^4=24,那么x-y=?
如果x+y=3,x^2+y^2=6,x^4-y^4=24,那么x-y=?

如果x+y=3,x^2+y^2=6,x^4-y^4=24,那么x-y=?
x^4-y^4=24
(x^2+y^2)(x^2-y^2)=24
(x^2+y^2)(x+y)(x-y)=24
6*3*(x-y)=24
x-y=4/3

x^4-y^4
=(x²+y²)(x+y)(x-y)
=6×3(x-y)
则18(x-y)=24
x-y=24÷18=4/3

∵x^4-y^4=24
∴(x²+y²)(x²-y²)=24
∵x^2+y^2=6
∴x²-y²=(x+y)(x-y)=4
∵x+y=3
x-y=4÷3=4/3