Question

IF a = 1- √2, then the value of (a - 1by a)^3 is​

Answer 1

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

$\mathcal\orange{To\:find \: \frac{a - 1}{a}}^3$

$\pink{Substituting\:the\:values}$

$\frac{1 - \sqrt{2} - 1}{1 - \sqrt{2} }$

$\frac{ \sqrt{ - 2} }{1 - \sqrt{2} }$

$Multiplying\:both\:sides\:by\:(1 + \sqrt{2} ) \: we \: get$

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

$\frac{ \sqrt{ - 2} - 2}{ - 1}$

$( \sqrt{2} + 2)$