Question

the answer is 50 but how pls give my answer pls ​

Answer 1

➫Question :-

$\sf \: what \: is \: the \: value \: of \: {p}^{2} + \frac{1}{4 {p}^{2} } \: \: if \: \\ \sf \: p - \frac{1}{2p} = 7 \:$

➫Answer :-

$\implies \: \boxed{ \sf {p}^{2} + \frac{1}{4 {p}^{2} } = 50}$

➫To Find :-

$\implies \sf {p}^{2} + \frac{1}{4 {p}^{2} }$

➫Solution :-

We have ,

$\mapsto \sf \: p - \frac{1}{2p} = 7 \: \\ \\ \sf \red{squaring \: on \: both }\: sides \: \\ \\ \mapsto \sf { \bigg \{p - \frac{1}{2p} \bigg \} }^{2} = {7}^{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \because \sf {(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy} \\ \\ \mapsto \sf {p}^{2} + { \bigg( \frac{1}{2p} \bigg) }^{2} - 2 \times p \times \frac{1}{2p} = 49 \\ \\ \mapsto \sf {p}^{2} + \frac{1}{4 {p}^{2} } - 1 = 49 \\ \\ \mapsto \sf {p}^{2} + \frac{1}{4 {p}^{2} } = 49 + 1 \\ \\ \mapsto \boxed{ \sf {p}^{2} + \frac{1}{4 {p}^{2} } = 50}$