The correct option is B 8 x = √(2) 1 1/x = 1/√(2) 1×√(2)+1/√(2)+1 =√(2)+1/(√(2))^2 (1)^2 =√(2)+1/2 1 =√(2)+1 =x 1/x = √(2) 1 √(2) 1 = 2 =(x 1/x)^3=( 2)^3 ...

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Byju's Answer

Standard IX

Mathematics

Rationalising Factor

If x=√2-1x-1/...

Question

If $x = \sqrt{2} - 1 (x - \frac{1}{x})^{3}$ = ______

-8

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Solution

The correct option is A
-8

$x = \sqrt{2} - 1$

$\frac{1}{x} = \frac{1}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}$

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

= $\sqrt{2} + 1$

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

= $- 2$

= $(x - \frac{1}{x})^{3} = (- 2)^{3}$

= $- 8$

Hence (A)

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If x=√2−1(x−1x)3 = ______

The correct option is A -8 x=√2−1 1x=1√2−1×√2+1√2+1 =√2+1(√2)2−(1)2 =√2+12−1 =√2+1 =x−1x=√2−1−√2−1 =−2 =(x−1x)3=(−2)3 = −8 Hence (A)

If $x = \sqrt{2} - 1 (x - \frac{1}{x})^{3}$ = ______