(k-1)^3 -3*(-k^2 + k -2)*(k-1)>0
=>(K-1)(K^2-2K+1+3K^2-3K+6)>0
=>(K-1)(4K^2-5K+7)>0
TH1 [tex]\left\{\begin{matrix} K-1> 0 & & \\ 4K^{2}-5K+7> 0& & \end{matrix}\right.[/tex]
TH2 [tex]\left\{\begin{matrix} K-1<0 & & \\ 4K^2-5K+1<0 & & \end{matrix}\right.[/tex]