A) \[\frac{1}{3}\]
B) \[\frac{1}{4}\]
C) \[\frac{7}{2}\]
D) \[4\]
Correct Answer: B
Solution :
Since, \[\alpha ,\,\,\beta \] are the roots of the equation \[8{{x}^{2}}-3x+27=0\] \[\therefore \] \[\alpha +\beta =\left( -\frac{3}{8} \right)=\frac{3}{8}\] \[\alpha \beta =\frac{27}{8}={{\left( \frac{3}{2} \right)}^{3}}\] Now, \[{{\left( \frac{{{\alpha }^{2}}}{\beta } \right)}^{1/3}}+{{\left( \frac{{{\beta }^{2}}}{\alpha } \right)}^{1/3}}\] \[=\frac{{{\alpha }^{2/3}}\cdot {{\alpha }^{1/3}}+{{\beta }^{2/3}}\cdot {{\beta }^{1/3}}}{{{(\alpha \beta )}^{1/3}}}\] \[=\frac{\alpha +\beta }{{{(\alpha \beta )}^{1/3}}}\] \[=\frac{\frac{3}{8}}{{{\left( \frac{27}{8} \right)}^{1/3}}}=\frac{3}{8}\cdot \frac{2}{3}=\frac{1}{4}\]
You need to login to perform this action.
You will be redirected in
3 sec
