| If \[m-5n=2,\] then the value of\[({{m}^{3}}-125{{n}^{3}}-30\,\,mn)\]is [SSC (CGL) 2015] |
A) 6
B) 7
C) 8
D) 9
Correct Answer: C
Solution :
| Given, \[m-5n=2\] ... (i) |
| On cubing both sides, we get |
| \[{{(m-5n)}^{3}}={{(2)}^{3}}\] |
| \[\Rightarrow \]\[{{m}^{3}}-125{{n}^{3}}-3\,\,(m)(5n)(m-5n)=8\] |
| \[\Rightarrow \]\[{{m}^{3}}-125{{n}^{3}}-15mn\,\,(2)=8\] [from Eq, (i)] |
| \[\Rightarrow \]\[{{m}^{3}}-125{{n}^{3}}-30mn=8\] |
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