Question

已知方程(a-1)x^2-(a^2+1)x+a^2+a=0的根是正整数，求a的整数值。

Answer 1

a=1时x=1符合题意
a不等于1时,
( (a - 1) x - (a + 1))(x - a)=0
x=a或x=(a+1)/(a-1)
(a+1)/(a-1)=1+2/(a-1)为正整数只有a=2或3符合,同时也满足x=a这个根也为正整数
故a=1或2或3

Answer 2

( (a - 1) x - (a + 1))(x - a)=0
(a+1)/(a-1)=1+2/(a-1)为正整数
a=2, 3