若a^m+1 b^n+2·(a^2n-1·b)=a^5 b^3,求m+n的值

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若a^m+1b^n+2·(a^2n-1·b)=a^5b^3,求m+n的值若a^m+1b^n+2·(a^2n-1·b)=a^5b^3,求m+n的值若a^m+1b^n+2·(a^2n-1·b)=a^5b^

若a^m+1 b^n+2·(a^2n-1·b)=a^5 b^3,求m+n的值
若a^m+1 b^n+2·(a^2n-1·b)=a^5 b^3,求m+n的值

若a^m+1 b^n+2·(a^2n-1·b)=a^5 b^3,求m+n的值
解析:
因为a^(m+1) b^(n+2)·a^(2n-1)·b
=a^(m+1+2n-1)·b^(n+2+1)
=a^(m+2n)·b^(n+3)
=a^5 b^3
所以可得:
n+3=3,m+2n=5
解得n=0,m=5
所以:m+n=5

a^(m+1+2n-1)×b^(n+2+1)=a^5 b^3
∴m+1+2n-1=5 n+2+1=3
解得:{m=5 n=0
m+n=5+0=5