| 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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