# Clean Minima

Algebra Level 3

Let $$\large \alpha$$ and $$\large\beta$$ be the roots of $$x^{2}-4(k^{2}-7k+8)x-7$$.

If $$\large V_{n}=\alpha^{n}-\beta^{n}$$ for $$n\geq1$$.

Then Find the minimum possible value of

$\large\dfrac{V_{101}-7V_{99}}{V_{100}}$

×