Question

已知m^2=2n+1,4n^2=m+1(m不等于2)求m+2n 4n^3-mn+2n^2，

要详细过程顺便说明下原因谢谢

Answer 1

m^2=2n+1 ①
4n^2=m+1 ②
①-② 得 m^2-4n^2=2n-m
(m+2n)(m-2n)=-(m-2n)
(m-2n)(m+2n+1)=0
当 m=2n时 ①②方程相同，n为任意值，假设n=1,m=2同题意不合，舍去
故 m+2n=-1
4n^3-mn+2n^2=(m+1)n-mn+(m+1)/2
=mn+n-mn+m/2+1/2
=(m+2n)/2+1/2
=-1/2+1/2
=0