Question

若（a的m+1次方乘以b的n+2次方）乘以（a的2n-1次方乘以b的2m次方）=a的5次方b的3次方，求m+n的值

Answer 1

根据两边等式a、b次数守恒有m+1+2n-1=5,n+2+2m=3，求得n=3，m=-1

Answer 2

[a^(m+1)*b^(n+2)]*[a^(2n-1)*b^2m]=a^5b^3
a^(m+1)*b^(n+2)*a^(2n-1)*b^2m=a^5b^3
a^(m+1)*a^(2n-1)*b^(n+2)*b^2m=a^5b^3
a^[(m+1)+(2n-1)]b^(n+2+2m)=a^5b^3
a^(m+2n)b^(n+2+2m)=a^5b^3
m+2n=5
n+2+2m=3
解得
m=-1
n=3

m+n=-1+3=2