Quadratic EquationHard

Question

Let ' p ' is a root of the equation $x^{2} - x - 3 = 0$. Then the value of $\frac{p^{3} + 1}{p^{5} - p^{4} - p^{3} + p^{2}}$ is equal to

Options

A.$\frac{4}{3}$
B.$\frac{4}{9}$
C.$\frac{2}{9}$
D.$\frac{2}{3}$

Solution

$\frac{p^{3} + 1}{\left( p^{4} - p^{2} \right)(p - 1)} = \frac{(p + 1)\left( p^{2} - p + 1 \right)}{p^{2}(p - 1)^{2}(p + 1)} = \frac{p^{2} - p + 1}{\left( p^{2} - p \right)^{2}} = \frac{3 + 1}{(3)^{2}} = \frac{4}{9}$

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