Question

若2007x+y=3011,x+2007y=1005,求(x+y)的平方+(x-y)的3次方的值?

Answer 1

2007x+y=3011

x+2007y=1005

两式相加得

2008x+2008y=4016

2008(x+y)=4016

x+y=2

两式相减得

2006x-200y=2006

2006(x-y)=2006

x-y=1

(x+y)的平方+(x-y)的3次方

＝2²+1³

=4+1

=5