| Given that \[{{x}^{3}}+{{y}^{3}}=72\]and \[xy=8\] with \[x>y\] then the value of \[x-y\] is [SSC (CGL) 2015] |
A) \[4\]
B) \[2\]
C) \[-\,\,2\]
D) \[-\,\,4\]
Correct Answer: B
Solution :
| Given, \[{{x}^{3}}+{{y}^{3}}=72\] ...(i) |
| \[xy=8\] ... (ii) |
| By solving Eqs. (i) and (ii), we get |
| \[x=4,\]\[y=2\] |
| or \[x=2,\] \[y=4\] |
| But, \[x>y\] |
| \[\therefore \] \[x=4,\]\[y=2\] |
| \[\Rightarrow \] \[x-y=2\] |
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