Question

find the value of x solve it

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 7 \\ ( {x)}^{2} + 2x( \frac{1}{x} ) + ( \frac{1}{ {x}^{2} } ) - 2 = 7 \\ ( {x + \frac{1}{x}) }^{2} - 2 = 7 \\ ( {x + \frac{1}{x}) }^{2} = 9 \\ (x + \frac{1}{x} ) = \sqrt{9} = 3 \\ ( {x}^{3} + \frac{1}{ {x}^{3} }) = (x + \frac{1}{x} )( {x}^{2} - 1 + \frac{1}{ {x}^{2} } ) \\ add \: and \: subtract \: 2 \: to \: make \: it \: perfect \: square \\ = 3( ({x + \frac{1}{x} )}^{2} - 3) \\ = 3(( {3})^{2} - 3) \\ = 3( 9- 3) \\ = 3(6) \\ = 18$