SATHEE: Quantitative Aptitude Ques 1705

Quantitative Aptitude Ques 1705

Question: If $ ( x^{2}+\frac{1}{x^{2}} )=\frac{17}{4}, $ then what is $ ( x^{3}-\frac{1}{x^{3}} ) $ equal to?

Options:

A) $ \frac{75}{16} $

B) $ \frac{63}{8} $

C) $ \frac{95}{8} $

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

$ ( x^{2}+\frac{1}{x^{2}} )=\frac{17}{4} $

$ \Rightarrow $ $ x^{2}+\frac{1}{x^{2}}+2-2=\frac{17}{4} $

$ \Rightarrow $ $ {{( x-\frac{1}{x} )}^{2}}+2=\frac{17}{4} $

$ \Rightarrow $ $ {{( x-\frac{1}{x} )}^{2}}=\frac{17}{4}-2 $
$ \Rightarrow $ $ ( x-\frac{1}{x} )=\frac{3}{2} $ On cubing both sides, we get $ {{( x-\frac{1}{x} )}^{3}}={{( \frac{3}{2} )}^{3}} $

$ \Rightarrow $ $ x^{3}-\frac{1}{x^{3}}-3\times \frac{1}{x}\cdot x( x-\frac{1}{x} )=\frac{27}{8} $

$ \Rightarrow $ $ x^{3}-\frac{1}{x^{3}}=\frac{27}{8}+3\times ( \frac{3}{2} ) $

$ \Rightarrow $ $ x^{3}-\frac{1}{x^{3}}=\frac{27}{8}+\frac{9}{2} $
$ \Rightarrow $ $ ( x^{3}-\frac{1}{x^{3}} )=\frac{63}{8} $

Quantitative Aptitude Ques 1704

Quantitative Aptitude Ques 1706

Quantitative Aptitude Ques 1705

Question: If $ ( x^{2}+\frac{1}{x^{2}} )=\frac{17}{4}, $ then what is $ ( x^{3}-\frac{1}{x^{3}} ) $ equal to?

Options:

Answer:

Solution:

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