已知2m^2-5m-1=0,n^2+5n-2=0 ,求(mn+m+1)⼀n

2025-05-15 13:51:26
推荐回答(1个)
回答1:

2m^2-5m-1=0
n^2+5n-2=0
两边同时除以n^2
1+5/n-2/n^2=0

即2(1/n)^2-5*(1/n)-1=0
那么m,1/n是方程
2x^2-5x-1=0的根,
若m≠1/n
那么m+1/n=5/2,m/n=-1/2
∴(mn+m+1)/n
=m+m/n+1/n
=5/2-1/2
=2
m=1/n时,mn=1

2m^2-5m-1=0

(mn+m+1)/n
=(2+m)*m
=m^2+2m
解方程求出m的值即可