SATHEE: Quantitative Aptitude Ques 919

Quantitative Aptitude Ques 919

Question: $ x+\frac{1}{2x}=2, $ then find the value of $ 8x^{2}+\frac{1}{x^{3}}. $

Options:

A) 48

B) 88

C) 40

D) 44

Show Answer

Answer:

Correct Answer: C

Solution:

Given, $ x+\frac{1}{2x}=2 $ On multiplying by 2 both sides, we get $ 2x+\frac{2}{2x}=4 $
$ \Rightarrow $ $ 2x+\frac{1}{x}=4 $ On cubing both sides, we get $ {{( 2x+\frac{1}{x} )}^{3}}=4^{3} $

$ \Rightarrow $ $ {{(2x)}^{3}}+{{( \frac{1}{x} )}^{3}}+3\times 2x\times \frac{1}{x}( 2x+\frac{1}{x} )=64 $ $ [\because {{(a+b)}^{3}}=a^{3}+b^{3}+3ab(a+b)] $

$ \Rightarrow $ $ 8x^{2}+\frac{1}{x^{3}}+3\times 2x\times \frac{1}{x}( 2x+\frac{1}{x} )=64 $

$ \Rightarrow $ $ 8x^{3}+\frac{1}{x^{3}}+6\times 4=64 $

$ \Rightarrow $ $ 8x^{3}+\frac{1}{x^{3}}=64-24=40 $

Quantitative Aptitude Ques 918

Quantitative Aptitude Ques 920

Quantitative Aptitude Ques 919

Question: $ x+\frac{1}{2x}=2, $ then find the value of $ 8x^{2}+\frac{1}{x^{3}}. $

Options:

Answer:

Solution:

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