Question

please.....its urgent ​

Answer 1

$</p><p></p><p>\bold{\underline{\sf Given:}} </p><p>\\ </p><p> \sf \rightarrow \quad a - \frac{1}{a} = 3 </p><p></p><p>\\ \\</p><p></p><p>$

$</p><p></p><p>\bold{\underline{\sf To Find:}} </p><p>\\ </p><p> \sf \rightarrow \quad a^{2} + 3a + \frac{1}{a^{2}} - \frac{3}{a} \\ \\ </p><p>$

$</p><p>\bold{\underline{\sf Solution:}} </p><p>\\ \\</p><p>$

$</p><p>\sf \rightarrow \quad a - \frac{1}{a} = 3 \\ \\ \sf \quad square \: both \: sides \\ \\ \sf \rightarrow \quad \bigg(a - \frac{1}{a} \bigg)^{2} = ( {3)}^{2} \\ \\ \sf \rightarrow \quad {a}^{2} + \frac{1}{ {a}^{2} } - 2 \cdot \cancel{a} \cdot \frac{1}{ \cancel{a}} = 9 \\ \\ \sf \rightarrow \quad {a}^{2} + \frac{1}{ {a}^{2} } = 11 \qquad ...(1) \\ \\ </p><p>$

$</p><p>\sf \quad according \: to \: the \: question. \\ \\ \sf \rightarrow \quad {a}^{2} + 3a + \frac{1}{ {a}^{2} } - 3a = \: ? \\ \\ \sf \rightarrow \quad {a}^{2} + \frac{1}{ {a}^{2} } + 3 \bigg(a - \frac{1}{a} \bigg) \\ \\ \sf \rightarrow \quad 11 + 3\bigg(a - \frac{1}{a} \bigg) \quad \{ \: from \: (1) \: \} \\ \\ \sf \rightarrow \quad 11 + 3 \times 3 \quad \{ \: given, \: \bigg( a - \frac{1}{a} \bigg) = 3\: \} \\ \\ \sf \rightarrow \quad 11 + 9 \\ \\ \sf \rightarrow \quad 20</p><p>$