Math, asked by apurvsemwaal, 10 months ago

plasma tell fast both parts a and b​

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Answered by Laxmsharma03
2

Hey!!!

Refer to above attachment for explanation and answer

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Answered by DrNykterstein
1

</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>

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