已知2m-3n-p=0,3n+m=14p(p≠0),则m^2+3mn／n^2+p^2的值为_______.

题目

已知2m-3n-p=0,3n+m=14p(p≠0),则m^2+3mn／n^2+p^2的值为_______.

答案

2m-3n-p=0
3n+m=14p
解方程组得:m=5p,n=3p
m^2+3mn=m(m+3n)=14pm=14p*5p=70p^2
n^2+p^2=9p^2+p^2=10p^2
(m^2+3mn)／(n^2+p^2)=70p^2/10p^2=7