第一題.∵m²+m-1=0
∴m²+m=1-----------①
m³+2m²+2007
=m(m²+m)+m²+2007
把①式代入得
m+m²+2007
=1+2007
=2008
第二題.2ac+2bd+2ad+2bc=4006
a²+c²+b²+d²+2ac+2bd-a²-c²-b²-d²+2ad+2bc=4006
(a+c)²+(b+d)²-(a-d)²-(b-c)²=4006
(a+c-a+d)(a+c+a-d）+(b+d-b+c)(b+d+b-c)=4006
(c+d)(2a+c-d)+(c+d)(2b-c+d)=4006
(c+d)(2a+2b)=4006
(a+b)(c+d)=2003
∵a,b,c,d均為非負(fù)整數(shù),
2003為質(zhì)數(shù),2003=1*2003
∴a+b=1,c+d=2003
或a+b=2003,c+d=1
∴a+b+c+d=2004