若(am+1bn+2）（a2n-1b2n)=a5b3则求m+n的值

Question

若(a m+1 b n+2）（a 2n-1 b 2n )=a5 b3 则求m+n的值

Answer 1

a^(m+1)*b^(n+2)*a^(2n-1)*b^2m
=a^(m+1+2n-1)*b^(n+2+2m)
=a^(m+2n)*b^(2m+n+2)
=a^3*b^5
所以
m+2n=3……①
2m+n+2=5……②
由2m+n+2=5可得2m+n=3……③
①+③可得
3(m+n)=6
所以m+n=2