If-x3-1-x3-14-then-x-1-x- 4325

The correct option is C 2 (x 1/x )^3=x^3 1/x^3 3(x 1/x )=14 3(x 1/x ) Let x 1/x=a, then a^3=14 3a⇒ a^3+3a 14=0 Factors of 14=±1,±2,±7 Let a=+1, then 1+3 1 ...

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Byju's Answer

Standard IX

Mathematics

Algebraic Identities

If x3-1/x3=14...

Question

$I f x^{3} - \frac{1}{x^{3}} = 14, t h e n x + \frac{1}{x}$ =

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Solution

The correct option is D
2

${(x - \frac{1}{x})}^{3} = x^{3} - \frac{1}{x^{3}} - 3 (x - \frac{1}{x}) = 14 - 3 (x - \frac{1}{x}) L e t x - \frac{1}{x} = a, t h e n a^{3} = 14 - 3 a \Rightarrow a^{3} + 3 a - 14 = 0 F a c t o r s o f - 14 = \pm 1, \pm 2, \pm 7 L e t a = + 1, t h e n 1 + 3 - 14 \neq 0 L e t a = - 1, t h e n - 1 - 3 - 14 \neq 0 L e t a = 2, t h e n 8 + 6 - 14 = 0 ∴ x - \frac{1}{x} = 2$

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If x3−1x3=14, then x+1x=

The correct option is D 2 (x−1x)3=x3−1x3−3(x−1x)=14−3(x−1x)Let x−1x=a, thena3=14−3a⇒ a3+3a−14=0Factors of −14=±1,±2,±7Let a=+1, then 1+3−14≠0Let a=−1, then −1−3−14≠0Let a=2, then 8+6−14=0∴ x−1x=2

$I f x^{3} - \frac{1}{x^{3}} = 14, t h e n x + \frac{1}{x}$ =