如果(a^m+1*b^n+2)*(a^2n-1*b^2m)=a^5*b^3,求m+n^为平方符号.*为乘号.

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/25 23:41:46
如果(a^m+1*b^n+2)*(a^2n-1*b^2m)=a^5*b^3,求m+n^为平方符号.*为乘号.如果(a^m+1*b^n+2)*(a^2n-1*b^2m)=a^5*b^3,求m+n^为平方

如果(a^m+1*b^n+2)*(a^2n-1*b^2m)=a^5*b^3,求m+n^为平方符号.*为乘号.
如果(a^m+1*b^n+2)*(a^2n-1*b^2m)=a^5*b^3,求m+n
^为平方符号.*为乘号.

如果(a^m+1*b^n+2)*(a^2n-1*b^2m)=a^5*b^3,求m+n^为平方符号.*为乘号.
(a^m+1×b^n+2)×(a^2n-1×n^2m)
=a^m+1×a^2n-1×b^n+2×b^2m
=a^(m+1+2n-1)×b^(n+2+2m)
=a^(m+2n)×b^(2m+n+2)
所以
a^(m+2n)×b^(2m+n+2)=a^5×b³
所以有:
m+2n=5 (1) 且
2m+n+2=3 (2)
(1)+(2)得:
3m+3n=6
3(m+n)=6
所以
m+n=2