Question

若方程(x-1)/(x-3)=m/（x²-9）产生增根，则m的值为（ ）

Answer 1

两边乘(x+3)(x-3)
(x-1)(x+3)=m
增根则公分母为0
所以x=-3,x=3

x=-3
代入(x-1)(x+3)=m
0=m

x=3
代入(x-1)(x+3)=m
12=m

所以m=0,m=12

Answer 2

(x-1)/(x-3)=m/（x²-9）
(x-1)(x^2-9) = m(x-3)
(x-1)(x-3)(x+3) = m(x-3)
(x-3)[(x-1)(x+3) -m] =0
(x-3)(x^2+2x -(3+m) ) = 0
真根
△≥ 0
4 + 4(3+m) ≥ 0
4+12+4m ≥ 0
m ≥ -4