Question

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Answer 1

Answer: -128√2

Step-by-step explanation:

$x = 3 - 2\sqrt{2}$

First, we have to find the value of (x - 1/x).

$x - \dfrac{1}{x}$

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

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

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

$= (3-2\sqrt{2}) - \dfrac{(3+2\sqrt{2}) }{9 - 8 }$

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

$= 3-2\sqrt{2} - 3-2\sqrt{2}$

$= -4\sqrt{2}$

Now, we can find (x - 1/x)³.

$(x - \dfrac{1}{x})^{3}$

$= (-4\sqrt{2})^{3}$

$= (-4\sqrt{2})(-4\sqrt{2})(-4\sqrt{2})$

$= (-4)(-4)(-4)(\sqrt{2})(\sqrt{2}) (\sqrt{2})$

$= -64(2\sqrt{2})$

$= -128\sqrt{2}$

Answer 2

Answer:

-128√2

Step-by-step explanation:

x = 3 -2√2

1/x = 1/(3 -2√2)

1/x = 3 +2√2

(x - 1/x)³ = { 3 -2√2-3-2√2}³

= (-4√2)³

=-4√2 × -4√2 × -4√2

= -128√2