Question

If p-q=6 and PQ=10 find the value of (p+q)^2

Answer 1

$\sf \: Solution$

$\sf {(p - q)}^{2} = {p}^{2} + {q}^{2} - 2pq$

$\sf {6}^{2} = {p}^{2} + {q}^{2} - 2(10)$

$\sf \: 36 = {p}^{2} + {q}^{2} - 20$

$\sf \: 36 + 20 = {p}^{2} + {q}^{2}$

$\sf {p}^{2} + {q}^{2} = 56$

Now,

$\bf {(p + q)}^{2} = {p}^{2} + {q}^{2} + 2pq$

$\sf {(p + q)}^{2} = 56 + 20 = \pink{ 76}$