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If \( \Large x+\frac{1}{x}=\sqrt{3} \), then \( \Large x^{3}+\frac{1}{x^{3}} \) is equal to

A) 0
B) 1
C) 3
D) \( \Large \left(x+1\right) \)

Correct Answer:

A) 0

Description for Correct answer:

Given : \( \Large x+\frac{1}{3}=\sqrt{3} \)

Taking cube on both sides, we have

\( \Large \left(x+\frac{1}{x}\right)^{3}= \left(\sqrt{3}\right)^{3} \)

=> \( \Large x^{3} + \frac{1}{x^{3}} + 3x^{2}\frac{1}{x} + 3x\frac{1}{x^{2}} = 3\sqrt{3} \)

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

=> \( \Large x^{3}+\frac{1}{x^{3}}+3 \times \sqrt{3} = 3\sqrt{3} \)

=> \( \Large x^{3}+\frac{1}{x^{3}} = 0 \)

Part of solved Polynomials questions and answers : >> Elementary Mathematics >> Polynomials

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Similar Questions

1). One of the factors of \( \Large x^{3}+6x^{2}+11x+6 \) is

A). \( \Large \left(x-\frac{1}{2}\right) \)

B). \( \Large \left(x+\frac{1}{2}\right) \)

C). \( \Large \left(x-1\right) \)

D). \( \Large \left(x+1\right) \)

2). If polynomial \( \Large x^{3}-3x^{2}+kx+42 \) is divisible by \( \Large x+3 \), then value of k will be

A). 4

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A). 1, \( \Large x - 2 \)

B). \( \Large x - 2 \), 8

C). \( \Large x - 2 \), \( \Large x + 2 \)

D). \( \Large x - 2 \), \( \Large x^{2}-4 \)

4). If \( \Large a+b+c=0 \), thena \( \Large a^{3}+b^{3}+c^{3} \) is equal to

A). \( \Large a^{2} \left(b+c\right)+b^{2} \left(c+a\right)+c^{2} \left(a+b\right) \)

B). \( \Large 3 \left(b+c\right) \left(c+a\right) \left(a+b\right) \)

C). \( \Large 3 abc \)

D). \( \Large 6 a^{2}b^{2}c^{2} \)

5). If \( \Large a^{m^{n}}= \left(a^{m}\right)^{n} \), then the value of m is

A). n

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6). Value of \( \Large \left(X^{b-c}\right)^{b+c},\ \left(X^{c-a}\right)^{c+a},\ \left(X^{a-b}\right)^{a+b} \) is

A). 0

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7). If \( \Large 2^{x}=4^{y}=8^{z} and \frac{1}{2x}+\frac{1}{4y}+\frac{1}{6z}=\frac{24}{7} \), then value of z is

A). \( \Large \frac{7}{16} \)

B). \( \Large \frac{7}{32} \)

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8). Which one of the following is a polynomial?

A). \( \Large x^{3}+\sqrt{3x^{2}}+4\sqrt{x} \)

B). \( \Large x^{6}+2\sqrt{x^{2}}+x^{-1} \)

C). \( \Large x^{5}+x^{4}+x^{-1}+x^{-5} \)

D). \( \Large x^{3}+\sqrt{5x^{2}}+x+\sqrt{3} \)

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A). \( \Large X^{\frac{x}{y}} \)

B). \( \Large X^{ \left(\frac{x}{y}\right)-1 } \)

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10). If \( \Large x+\frac{1}{x}=3 \), then value of \( \Large x^{3}+\frac{1}{x^{3}} \) is

A). 18

B). 24

C). 27

D). 36