Question

已知,a,b满足a+b=-2014,ab=5,求(aa+2013a+4)(bb+2015b+6）的值

Answer 1

2013a=[-(a+b)-1]a=-aa-ab-a

2015b=[-(a+b)+1]b=-ab-bb+b

∴原式=(aa-aa-ab-a+4)(bb-ab-bb+b+6)

=(-ab-a+4)(-ab+b+6)

=(-5-a+4)(-5+b+6)

=-(a+1)(b+1)

=-ab-(a+b)-1

=-5+2014-1

=2008