已知(x+y)^2=7,(x-y)=3.求x^4+y^4的值;x^6+y^6的值.

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已知(x+y)^2=7,(x-y)=3.求x^4+y^4的值;x^6+y^6的值.
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已知(x+y)^2=7,(x-y)=3.求x^4+y^4的值;x^6+y^6的值.
已知(x+y)^2=7,(x-y)=3.求x^4+y^4的值;x^6+y^6的值.

已知(x+y)^2=7,(x-y)=3.求x^4+y^4的值;x^6+y^6的值.
题目打错了吧 应该是（x-y)^2=3吧?
如果这样
则
(x+y)²=7
x²+y²+2xy=7 (1)
(x-y)²=x²+y²-2xy=3 (2)
(1)+(2)
2(x²+y²)=10
x²+y²=5
(1)-(2)
4xy=4
xy=1
x²+y²=5
平方
x^4+y^4+2x²y²=25
x^4+y^4=25-2(xy)²=23
x^6+y^6
=(x²+y²)(x^4-x²y²+y^4)
=5*(23-1²)
=110

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