Question

If x=3-2√2,findx3-1/x3

Answer 1

●••••••••• Hello User •••••••••●

《《Here is your answer 》》
___________________________

$given \: . \\ \\ x = 3 - 2 \sqrt{2} \\ \\ \frac{1}{x} = \frac{1}{3 - 2 \sqrt{2} } \\ \\ = \frac{1}{3 - 2 \sqrt{2} } \times \frac{3 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } \\ \\ = \frac{3 + 2 \sqrt{2} }{ {(3)}^{2} - {(2 \sqrt{2}) }^{2} } \\ \\ = \frac{3 + 2 \sqrt{2} }{9 - 4 \times 2} \\ \\ = \frac{3 + 2 \sqrt{2} }{9 - 8} \\ \\ = 3 + 2 \sqrt{2} \\ \\ now \: .by \: using \: identity : \: \\ \\ = {a}^{3} - {b}^{3} \\ \\ = (a - b)( {a}^{2} + ab + {b}^{2}) \\ \\ then : \\ \\ = {x}^{3} - { (\frac{1}{x} )}^{3} \\ \\ = (x - \frac{1}{x})( {x}^{2} + x \times \frac{1}{x} + {( \frac{1}{x}) }^{2} ) \\ \\ putting \: the \: value \: of \: x \: and \: \frac{1}{x} \: w e \: get: \\ \\ = (3 - 2 \sqrt{2} - 3 - 2 \sqrt{2} )( {(3 - 2 \sqrt{2}) }^{2} + 1 + {(3 + 2 \sqrt{2}) }^{2} ) \\ \\ = (- 4 \sqrt{2} )(9 + 8 - 12 \sqrt{2} + 1 + 9 + 8 + 12 \sqrt{2}) \\ \\ = ( - 4 \sqrt{2} )( 35) \\ \\ = - 140 \sqrt{2}$
___________________________

《Hope it may helpful to you 》

••••••• @ajaman ^_^ ••••••••

●••☆ Brainly Star ☆••●