Question

若关于X的方程1\(x^2-x)+(k-5)\(x^2+x)=(k-1)\(x^2-1)的增根是X=1.求K的值

Answer 1

1(x^2-x)+(k-5)(x^2+x)=(k-1)(x^2-1)

方程两边同乘以（x-1)得

1x+(k-5)(x-1)(x^2+x)=(k-1)(x+1)

将x=1代入上式得

1=（k-1)2

k=3