15问答网 > 关于x的一元二次方程 （m-1）x^2 -2mx+m+1=0 。 m为何整数时，该方程的两个解为正整数.......

关于x的一元二次方程 （m-1）x^2 -2mx+m+1=0 。 m为何整数时，该方程的两个解为正整数.......

2025-02-11 21:49:28
推荐回答（1个）
回答1：

(m+1)/(m-1)>0

(m-1+2)/(m-1)>0

1+2/(m-1)>0

且为整数

所以

m-1=1或m-1=2

即m=2或m=3

  1. m=2

    代入，得

    x²-4x+3=0

    (x-1)(x-3)=0

    x=1或x=3成立；

  2. m=3

    代入，得

    2x²-6x+4=0

    x²-3x+2=0

    (x-1)(x-2)=0

    x=1或x=2

    成立。

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