If $0<\mathrm{p}<1$ then roots of the equation $(1-\mathrm{p}){\mathrm{x}}^2+4\mathrm{x}+\mathrm{p}=0$ are

If $\mathrm{x}>0$, the minimum value of $\frac{{\left(x+\frac{1}{x}\right)}^6-\left(x^6+\frac{1}{x^6}\right)-2}{{\left(x+\frac{1}{x}\right)}^3+\left(x^3+\frac{1}{x^3}\right)}\text{ is }$

Let a and b be the roots of the quadratic equation

$\mathrm{x}^\left\{2\right\}+3 \mathrm{x}-1=0 \text{if}$ ${\mathrm{P}}_{\mathrm{n}}={\mathrm{a}}^{\mathrm{n}}+{\mathrm{h}}^{\mathrm{n}}\text{ for }\mathrm{n}>0,\text{ then, for }\mathrm{n}>2,{\mathrm{P}}_{\mathrm{n}}=$