Question

given x-1/x=root over 15 find.x+1/x,x^2+1/x^2,x^2-1/x^2

Answer 1

Hope u like my process
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$= > \bf \: x - \frac{1}{x} = \sqrt{15} \\ \\ \bf \underline{squaring \: \: both \: \: sides} \\ \\ = > {(x - \frac{1}{x} )}^{2} = 15 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } - 2x. \frac{1}{x} = 15 \\ \\ = > \bf {x}^{2} + \frac{1}{ {x}^{2} } = 15 + 2 = \underline{ 17} \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 17 + 2 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2x. \frac{1}{x} = 19 \\ \\ = > {(x + \frac{1}{ {x} } )}^{2} = 19 \\ \\ = > \bf x + \frac{1}{x} = \underline{ \sqrt{19} } \\ \\ \\ now.. \\ \\ \\ = > \bf {x}^{2} - \frac{1}{ {x}^{2} } \\ \\ = (x - \frac{1}{x} )(x + \frac{1}{x} ) \\ \\ = \sqrt{15} \times \sqrt{19} \\ \\ = \bf \underline{ \sqrt{289} }$
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