设：x^2-2x-2k=t
则：t+(3k^2-9k)/t=3-4k
t^2+(4k-3)t+(3k^2-9k)=0
(t-3k)(t-(k-3))=0
t1=3k,t2=k-3
3k≠k-3,k≠-3/2
t=3k时
x^2-2x-2k=3k
x^2-2x-5k=0
判别式△=4+20k>0,k>-1/5
t=k-3时
x^2-2x-2k=k-3
x^2-2x-3k+3=0
判别式△=4+4(3k-3)=12k-8>0,k>2/3
所以,k的取值范围是,k>2/3