若2008x+2009y=2007,2009x+2008y=2010,求(x+y)的3次方+(x-y)的3次方的值

问题描述:

若2008x+2009y=2007,2009x+2008y=2010,求(x+y)的3次方+(x-y)的3次方的值

2008x+2009y=2007,2009x+2008y=2010
相加
4017x+4017y=4017
x+y=1
相减x-y=3
(x+y)^3+(x-y)^3
=1+27
=28

2008x+2009y=2007...(1)
2009x+2008y=2010...(2)
(1)+(2)
x+y=1
(2)-(1)
x-y=3
(x+y)的3次方+(x-y)的3次方
=1+27=28