Quantitative Aptitude Ques 2401

Question: If $ a={{(\sqrt{2}+1)}^{-1/3}}, $ then find out the value of $ ( a^{3}-\frac{1}{a^{3}} ). $

Options:

A) 0

B) $ -2\sqrt{2} $

C) $ 3\sqrt{2} $

D) $ -2 $

Show Answer

Answer:

Correct Answer: D

Solution:

  • $ a={{(\sqrt{2}+1)}^{-1/3}} $
    $ \Rightarrow $ $ a={{( \frac{1}{\sqrt{2}+1} )}^{1/3}} $ $ a^{3}=\frac{1}{\sqrt{2}+1}=\frac{1}{\sqrt{2}+1}\times \frac{(\sqrt{2}-1)}{(\sqrt{2}+1)}=\frac{\sqrt{2}-1}{1}=\sqrt{2}-1 $
    $ \therefore $ $ \frac{1}{a^{3}}=\frac{1}{\sqrt{2}-1}\times \frac{\sqrt{2}+1}{\sqrt{2}+1}=\sqrt{2}+1 $ So, $ a^{3}-\frac{1}{a^{3}}=\sqrt{2}-1-(\sqrt{2}+1) $ $ =\sqrt{2}-1-\sqrt{2}-1=-,2 $
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