Quantitative Aptitude Ques 2160

Question: If $ a+b+c=0, $ then find the value of

$ \frac{1}{a^{3}}+\frac{1}{b^{3}}+\frac{1}{c^{3}}+\frac{1}{{{(a+b)}^{3}}}+\frac{1}{{{(b+c)}^{3}}}+\frac{1}{{{(c+a)}^{3}}}. $

Options:

A) $ -1 $

B) $ 3abc $

C) 1

D) 0

Show Answer

Answer:

Correct Answer: D

Solution:

  • $ a+b+c=0 $ By putting a = 1, b = 0 and $ c=-1 $ $ =\frac{1}{{{(1)}^{3}}}+0+\frac{1}{{{(-1)}^{3}}}+\frac{1}{{{(1)}^{3}}}+\frac{1}{{{(-1)}^{3}}}+\frac{1}{(0)} $ $ =1+0-1+1-1+0=0 $
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