Question

please it is very urgent for me​

Answer 1

Question

$\mathsf{if \: a + \frac{1}{a} = p \: and \: a - \frac{1}{a} = q}$

Answer

We will add both the equations

$\mathcal{2a = p + q - - (1) } \\ \\ \sf{now \: subtracting \: both \: the \: equation} \\ \\ \mathcal{ \frac{2}{a} = p - q - - (2)} \\ \\ \sf{now \: substitutimg \: both \: the \: equation \: from \: (1) \: into \: (2)} \: \\ \\ \mathcal{ \frac{4}{(p + q) } = p - q } \\ \\ \mathcal{4 = {p}^{2} - {q}^{2} }$