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Please it is very urgent for me​

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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} }



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