| If \[a+b+c=0,\]then find the value of |
| \[\frac{1}{{{a}^{3}}}+\frac{1}{{{b}^{3}}}+\frac{1}{{{c}^{3}}}+\frac{1}{{{(a+b)}^{3}}}+\frac{1}{{{(b+c)}^{3}}}+\frac{1}{{{(c+a)}^{3}}}.\] [SSC (CGL) 2014] |
A) \[-1\]
B) \[3abc\]
C) 1
D) 0
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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