If \[m+n=-\,\,2,\]then the value of \[{{m}^{3}}+{{n}^{3}}-6,\]\[mn\]is |
A) \[8\]
B) \[4\]
C) \[-\,\,8\]
D) \[-\,\,4\]
Correct Answer: C
Solution :
Given, \[m+n=-\,\,2\] |
Now, \[{{m}^{3}}+{{n}^{3}}-6\,\,mn\] |
\[={{(m+n)}^{3}}-3\,\,mn\,\,(m+n)-6\,\,mn\] |
\[[\because {{a}^{3}}+{{b}^{3}}={{(a+b)}^{3}}-3ab\,\,(a+b)]\] |
\[={{(-\,\,2)}^{3}}-3\,\,mn\,\,(-\,\,2)-6\,\,mn\] |
\[=-\,8+6\,\,mn-6\,\,mn=-\,8\] |
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