Mathematics: I need 6th question in the paper

Seventy-five million three hundred thousand two hundred seven...

I need 6th question in the paper - id66797587, mstrish71oteauw

emmie50

28.01.2022

Step-by-step explanation:

$a = 1 - \sqrt{2}$

$(a - \dfrac{1}{a})^3 =$

$= (\dfrac{a^2}{a} - \dfrac{1}{a})^3$

$= (\dfrac{a^2 - 1}{a})^3$

$= (\dfrac{(a + 1)(a - 1)}{a})^3$

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

$= (\dfrac{(2 - \sqrt{2})(-\sqrt{2})}{1 - \sqrt{2}})^3$

$= (\dfrac{(-2\sqrt{2} + \sqrt{2}\sqrt{2}}{1 - \sqrt{2}})^3$

$= (\dfrac{2 - 2\sqrt{2}}{1 - \sqrt{2}})^3$

$= (\dfrac{2(1 - \sqrt{2})}{1 - \sqrt{2}})^3$

= 2^3

= 8

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