已知(x-y)^2=8,xy=2,求(x+y)^2,x^4+y^4的值

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已知(x-y)^2=8,xy=2,求(x+y)^2,x^4+y^4的值已知(x-y)^2=8,xy=2,求(x+y)^2,x^4+y^4的值已知(x-y)^2=8,xy=2,求(x+y)^2,x^4+

已知(x-y)^2=8,xy=2,求(x+y)^2,x^4+y^4的值
已知(x-y)^2=8,xy=2,求(x+y)^2,x^4+y^4的值

已知(x-y)^2=8,xy=2,求(x+y)^2,x^4+y^4的值
(x-y)^2=x^2+y^2-2xy=8
而xy=2 所以x^2+y^2=12
(x+y)^2=x^2+y^2+2xy=12+4=16
x^4+y^4=(x^2+y^2)^2-2x^2y^2
=12^2-2*2*2=144-8=136

(x-y)^2=x^2+y^2-2xy=8
而xy=2 所以x^2+y^2=12
(x+y)^2=x^2+y^2+2xy=12+4=16
x^4+y^4=(x^2+y^2)^2-2x^2y^2
=12^2-2*2*2=144-8=136

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