The integer ' k ', for which the inequality

$x^{2}-2(3 K-1) x+8 K^{2}-7>0$

Now, $D<0$

$\Rightarrow 4(3 K-1)^{2}-4 \times 1 \times\left(8 K^{2}-7\right)<0$

$\Rightarrow 9 K^{2}-6 K+1-8 K^{2}+7<0$

$\Rightarrow K^{2}-6 K+8<0$

$\Rightarrow(K-4)(K-2)<0$

$\Rightarrow \quad \mathrm{K} \in(2,4)$