Question

plasma tell fast both parts a and b​

Answer 1

Hey!!!

Refer to above attachment for explanation and answer

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Answer 2

$</p><p>\underline{\sf Given:}</p><p>\\ </p><p> \sf \rightarrow \quad x^{2} + \dfrac{1}{x^{2}} = 27 \\ \\</p><p>$

$</p><p>\underline{\sf ToFind:}</p><p>\\ </p><p> \sf (i) \quad x + \dfrac{1}{x}</p><p>\sf (ii) \quad x - \dfrac{1}{x} </p><p></p><p>\\ \\</p><p>$

$</p><p>\underline{\sf Solution:} \\ \\ \sf (i)</p><p> \\ \sf \rightarrow \quad \bigg( x + \dfrac{1}{x} \bigg)^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \cdot \cancel{x } \cdot \frac{1}{ \cancel{x} } \\ \\ \sf \rightarrow \quad \sqrt{ \bigg( x + \frac{1}{x} \bigg)^{2} } = \sqrt{27 + 2} \qquad \bigg( \because \: {x}^{2} + \frac{1}{ {x}^{2} } = 27 \: \bigg) \\ \\ \sf \Rightarrow \quad x + \frac{1}{x} = \sqrt{29} \\ \\ \sf (ii) \\ \sf \rightarrow \quad { \bigg( x - \frac{1}{x} \bigg)}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \cdot \cancel{x} \cdot \frac{1}{ \cancel{x}} \\ \\ \sf \rightarrow \quad \sqrt{ { \bigg( x - \frac{1}{x} \bigg)}^{2} } = 27 - 2 \qquad \bigg( \: \because \: {x}^{2} + \frac{1}{ {x}^{2} } = 27 \: \bigg) \\ \\ \sf \rightarrow \quad x - \frac{1}{x} = \sqrt{25} \\ \\ \sf \Rightarrow \quad x - \frac{1}{x} = 5</p><p>$