Question

关于x的方程(1-2k)x^2-2(k+1)-1/2k=0有实根

Answer 1

1）

方程只有一个实根

△=4(k+1)^2+4(1-2k)*1/2k=10k+4=0

k=-2/5

方程为：9x^2/5-6x/5+1/5=0

(3x-1)^2/5=0

x=1/3

2)

x1+x2=2(k+1)/(1-2k)

x1x2=-k/2(1-2k)

1/x1+1/x2=(x1+x2)/x1x2

=2(k+1)/(-k/2)

=-4(k+1)/k

=-6

6k=4k+4

k=2