已知m、n满足25^m210^n=5^7*2^4,求√(m^2+n^2)的值

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已知m、n满足25^m*2*10^n=5^7*2^4,求√(m^2+n^2)的值
已知m、n满足25^m*2*10^n=5^7*2^4,求√(m^2+n^2)的值

已知m、n满足25^m*2*10^n=5^7*2^4,求√(m^2+n^2)的值
25^m*2*10^n=5^7*2^4
5^2m*2^(n+1)*5^n=5^7*2^4
2m+n=7
n+1=4
m=2
n=3
将m,n分别代入即可求得√(m^2+n^2)的值

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