SATHEE: Quantitative Aptitude Ques 523

Quantitative Aptitude Ques 523

Question: If $ x^{4}+\frac{1}{x^{4}}=727, $ then find the value of $ x^{3}-\frac{1}{x^{3}}. $

Options:

A) 140

B) 120

C) 190

D) 160

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $ x^{4}+\frac{1}{x^{4}}=727 $ Add 2 on both side, we get, $ x^{4}+\frac{1}{x^{4}}+2=727+2 $

$ \Rightarrow $ $ {{( x^{2}+\frac{1}{x^{2}} )}^{2}}=729 $
$ \Rightarrow $ $ x^{2}+\frac{1}{x^{2}}=\sqrt{729} $

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

$ \Rightarrow $ $ ,x-\frac{1}{x}=\sqrt{25} $
$ \Rightarrow $ $ x-\frac{1}{x}=5 $

$ \therefore $ $ {{( x-\frac{1}{x} )}^{3}}=x^{3}-\frac{1}{x^{3}}-3,( x-\frac{1}{x} ) $ $ {{(5)}^{3}}=x^{3}-\frac{1}{x^{3}}-3\cdot (5) $

$ \Rightarrow $ $ x^{3}-\frac{1}{x^{3}}=125+15=140 $

Quantitative Aptitude Ques 522

Quantitative Aptitude Ques 524

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