Question

Plz answer to the Above!!!

Answer 1

$Given : a = 1 - \sqrt{2}$

$= > \frac{1}{a} = \frac{1}{1 - \sqrt{2}} * \frac{1 + \sqrt{2}}{1 + \sqrt{2}}$

$= > \frac{1 + \sqrt{2}}{(1)^2 - (\sqrt{2})^2}$

$= > \frac{1 + \sqrt{2}}{1 - 2}$

$= > \frac{1 + \sqrt{2}}{-1}$

$= > -(1 + \sqrt{2})$

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Now,

$= > (a - \frac{1}{a})^3 = (1 - \sqrt{2} + 1 + \sqrt{2})^3$

$= > 2^3$

$= > \boxed{8}}$

Hope this helps!

Answer 2

$\bf \large \it{Hey \: User!!!}$

given a = 1 - √2

$\bf \small \: therefore \: \frac{1}{a} = \frac{1}{1 - \sqrt{2} } \\ \bf \tiny by \: rationalising \: = > \frac{1}{1 - \sqrt{2} } \times \frac{1 + \sqrt{2} }{1 + \sqrt{2} } \\ \bf \small = \frac{1 + \sqrt{2} }{(1 - \sqrt{2} )(1 + \sqrt{2}) } \\ \\ \bf \small \: = \frac{1 + \sqrt{2} }{ {1}^{2} - { (\sqrt{2}) }^{2} } \\ \\ \bf \small = \frac{1 + \sqrt{2} }{1 - 2} \\ \\ \bf \small = \frac{1 + \sqrt{2} }{ - 1} \\ \\ \bf \small \: = - 1 + \sqrt{2}$

we have to find ( a - 1/a )³

$\bf = {(1 - \sqrt{2 } - ( - 1 + \sqrt{2}) }^{3} \\ \bf \: = {(1 - \sqrt{2} + 1 + \sqrt{2} ) }^{?} \\ \bf \: = {(2)}^{3} \\ \bf = 2 \times 2 \times \times 2 \\ \bf = 8$

$\bf \large \it{Cheers!!!}$