已知(x+y)^2=7 (x-y)^2=3计算x^6+y^6已知(x+y)^2=7 (x-y)^2=3计算x^6+y^6

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已知(x+y)^2=7(x-y)^2=3计算x^6+y^6已知(x+y)^2=7(x-y)^2=3计算x^6+y^6已知(x+y)^2=7(x-y)^2=3计算x^6+y^6已知(x+y)^2=7(x

已知(x+y)^2=7 (x-y)^2=3计算x^6+y^6已知(x+y)^2=7 (x-y)^2=3计算x^6+y^6
已知(x+y)^2=7 (x-y)^2=3计算x^6+y^6
已知(x+y)^2=7 (x-y)^2=3计算x^6+y^6

已知(x+y)^2=7 (x-y)^2=3计算x^6+y^6已知(x+y)^2=7 (x-y)^2=3计算x^6+y^6
(x+y)²=x²+2xy+y²=7
(x-y)²=x²-2xy+y²=3
两式相加,x²+y²=5
两式相减,xy=1
x^6+y^6
=(x²)³+(y²)³
=(x²+y²)(x^4-x²y²+y^4)
=5[(x²+y²)²-3xy]
=5×(25-3)
=110

答:
(x+y)^2=7
(x-y)^2=3
两式相加:
2x^2+2y^2=10,x^2+y^2=5
两式相减:
4xy=4,xy=1
x^6+y^6
=(x^2+y^2)(x^4-x^2y^2+y^2)
=5*[(x^2+y^2)^2-3(xy)^2]
=5*(5^2-3*1^2)
=5*(25-3)
=110
所以:x^6+y^6=110

(x+y)^2=7 (x-y)^2=3
两式相减
(x+y)^2-(x-y)^2=4
2x*2y=4
xy=1

x^2+y^2
=(x+y)^2-2xy
=7-2
=5
x^4+y^4
=(x^2+y^2)^2-2x^2y^2
=25-2
=23

x^6+y^6
=(x^2+y^2)(x^4-x^2y^2+y^4)
=5*(23-1)
=110