若(a^m+1)(b^n+1)(a^2n)(b^2m)=(a^5)(b^3),则m+n的值为A.1 B.2 C.3 D.-3
问题描述:
若(a^m+1)(b^n+1)(a^2n)(b^2m)=(a^5)(b^3),则m+n的值为
A.1 B.2 C.3 D.-3
答
(a^m+1)(b^n+1)(a^2n)(b^2m)=a^(m+1+2n)*b^(2m+n+1)=(a^5)(b^3).
m+1+2n=5,2m+n+1=3,m+2n=4(1),2m+n=2(2)
(2)+(1),3(m+n)=6,m+n=2