If x -1-2- find the value of x -1- x 3A- 13B- 14C- 8D- 22

The correct option is C 8 We have, x= 1 √(2) ∴1/x = 1/1 √(2) = 1/1 √(2)×1 + √(2)/1 + √(2) 1 + √(2)/(1)^2 (√(2))^2 = 1 + √(2)/1 2 = 1 + √(2)/ 1 = (1 ...

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Byju's Answer

Standard IX

Mathematics

Addition and Subtraction of Numbers with Square Root

If x =1-√2, f...

Question

If $x = 1 - \sqrt{2}$ , find the value of $(x - \frac{1}{x})^{3}$

$13$

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$14$

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$8$

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$2^{2}$

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Solution

The correct option is C
$8$

We have, $x = 1 - \sqrt{2}$
$∴ \frac{1}{x} = \frac{1}{1 - \sqrt{2}} = \frac{1}{1 - \sqrt{2}} \times \frac{1 + \sqrt{2}}{1 + \sqrt{2}} \frac{1 + \sqrt{2}}{(1)^{2} - (\sqrt{2})^{2}} = \frac{1 + \sqrt{2}}{1 - 2} = \frac{1 + \sqrt{2}}{- 1} = - (1 + \sqrt{2}) T h u s, x - \frac{1}{x} = (1 - \sqrt{2}) - (- (1 + \sqrt{2})) = 1 - \sqrt{2} + 1 + \sqrt{2} = 2 H e n c e, (x - \frac{1}{x})^{3} = 2^{3} = 8$

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If x=1−√2, find the value of (x−1x)3

The correct option is C 8 We have, x=1−√2 ∴1x=11−√2=11−√2×1+√21+√21+√2(1)2−(√2)2=1+√21−2=1+√2−1=−(1+√2)Thus,x−1x=(1−√2)−(−(1+√2))=1−√2+1+√2=2Hence,(x−1x)3=23=8

If $x = 1 - \sqrt{2}$ , find the value of $(x - \frac{1}{x})^{3}$