Question

please solve it i really need this urgently

Answer 1

$a = 3 - 2 \sqrt{2 } \\ \frac{1}{a} = \frac{1}{3 - 2 \sqrt{2} } \\ = \frac{(3 + 2 \sqrt{2}) }{(3 - 2 \sqrt{2})(3 + 2 \sqrt{2} ) } \\ = \frac{3 + 2 \sqrt{2} }{ {3}^{2} - {(2 \sqrt{2}) }^{2} } \\ = \frac{3 + 2 \sqrt{2} }{9 - 8} \\ = \frac{3 + 2 \sqrt{2} }{1} \\ = 3 + 2 \sqrt{2}$
$a - \frac{1}{a} = 3 - 2 \sqrt{2} - (3 + 2 \sqrt{2} ) \\ = 3 - 2 \sqrt{2 } - 3 - 2 \sqrt{2} \\ = - 4 \sqrt{2}$
$a + \frac{1}{a} = 3 - 2 \sqrt{2} + 3 + 2 \sqrt{2} \\ = 6$
${a}^{2} - \frac{1}{ {a }^{2} } = (a + \frac{1}{a} )(a - \frac{1}{a} ) \\ =( - 4 \sqrt{2} )(6) \\ = - 24 \sqrt{2}$
Hey buddy here is your answer...........