Question

solve for p and q:p+q/pq=2 and p-q/pq=6​

Answer 1

Answer :★ p = 1/2 and

★ q = 1/4

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Step by step Solution :

$\frac{p + q}{pq} = 2 \\ \\ \implies p + q = 2pq .....(1)\\ \\ and \\ \implies \frac{p - q}{pq} = 6 \\ \\ \implies \: p - q = 6pq......(2) \\ now \:adding \: (1) \: and \: (2) \\ \implies \: p + q + p - q = 2pq + 6pq \\ \\ \implies2p = 8pq \\ \\ \implies2p = 2p(4q) \\ \\ \implies4q = 1 \\ \\ \implies \: q = \frac{1}{4} \\ \\ using \: q = \frac{1}{4} in \: (1) \\ \implies \: p + \frac{1}{4} = 2p( \frac{1}{4} ) \\ \\ \implies \: p + \frac{1}{4} = \frac{p}{2} \\ \\ \implies \: p - \frac{p}{2} = - \frac{1}{4} \\ \\ \implies \frac{2p - p}{2} = \frac{1}{4} \\ \\ \implies \: \frac{p}{2} = \frac{1}{4} \\ \\ \implies \: p \: = \frac{2}{4} \\ \\ \implies \: p = \frac{1}{2}$