Question

$p ^{2} + \: q ^{2} \: \: \: if \: \: \: \: p - \: q = 6 \: and \: \: p + q = 14$
please tell me the answer with solutions. ​

Answer 1

$p + q = 14...(1) \\ p - q = 6...(2) \\ (1) + (2) \implies \: 2p = 20 \\ \implies \: p = 10 \\ (1) - (2) \implies \: 2q = 8 \\ \implies \: q = 4 \\ pq = 10 \times 4 = 40 \\ \\ Now \: \: \: \: {p}^{2} + {q}^{2} = ( {p + q})^{2} - 2pq \\ = ( {14})^{2} - 2 \times 40 \\ = 196 - 80 \\ = 116$