Answer:
8
Step-by-step explanation:
[tex] a = 1 - \sqrt{2} [/tex]
[tex] (a - \dfrac{1}{a})^3 = [/tex]
[tex] = (\dfrac{a^2}{a} - \dfrac{1}{a})^3 [/tex]
[tex] = (\dfrac{a^2 - 1}{a})^3 [/tex]
[tex] = (\dfrac{(a + 1)(a - 1)}{a})^3 [/tex]
[tex] = (\dfrac{(1 - \sqrt{2} + 1)(1 - \sqrt{2} - 1)}{a})^3 [/tex]
[tex]= (\dfrac{(2 - \sqrt{2})(-\sqrt{2})}{1 - \sqrt{2}})^3[/tex]
[tex]= (\dfrac{(-2\sqrt{2} + \sqrt{2}\sqrt{2}}{1 - \sqrt{2}})^3[/tex]
[tex]= (\dfrac{2 - 2\sqrt{2}}{1 - \sqrt{2}})^3[/tex]
[tex]= (\dfrac{2(1 - \sqrt{2})}{1 - \sqrt{2}})^3[/tex]
[tex] = 2^3 [/tex]
[tex] = 8 [/tex]
