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If \( \Large x^{3}-\frac{1}{x^{3}}=14 \), then value of \( \Large x-\frac{1}{x} \) will be

A) 2
B) 3
C) 4
D) 5

Correct Answer:

A) 2

Description for Correct answer:

\( \Large x^{3}-\frac{1}{x^{3}}=14 \)

=> \( \Large \left(x-\frac{1}{x}\right)^{3}+3x \times \frac{1}{x} \left(x-\frac{1}{x}\right)=14 \)

Put \( \Large x-\frac{1}{x}=z \)

Therefore, \( \Large z^{3}+3z-14=0 \)

Now, 2 = 2 satisfies the equation, hence (z - 2) factor. i.e.

z = 2

Therefore, \( \Large x-\frac{1}{x} = 2 \)

Part of solved Rational expression questions and answers : >> Elementary Mathematics >> Rational expression

Comments

Similar Questions

1). The value of \( \Large 2^{3^{2}} \) = ?

A). 1

B). 2

C). 8

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2). The value of \( \Large \left(2^{3/4}+2^{1/2}+2^{1/4}+1\right) \left(2^{1/4-1}\right) \) =?

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4). If \( \Large 2^{2x-1}=\frac{1}{8^{x-3}} \), then the value of x is

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5). \( \Large \left(32\right)^{.17} \times \left(32\right)^{.03} \) is equal to

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6). \( \Large \sqrt{144+256} \) is equal to

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