Question

# If $$\alpha ,\beta$$ are the roots of the equation $$2{ x }^{ 2 }-5x+16=0\quad$$ then the value of $$\quad { \left( \cfrac { { \alpha }^{ 2 } }{ \beta } \right) }^{ \cfrac { 1 }{ 3 } }+{ \left( \cfrac { { \beta }^{ 2 } }{ \alpha } \right) }^{ \cfrac { 1 }{ 3 } }$$ is :

A
14
B
54
C
13
D
512

Solution

## The correct option is B $$\cfrac { 5 }{ 4 }$$$$\alpha +\beta =\cfrac { 5 }{ 2 } ;\alpha \beta =8\quad$$$$\quad { \left( \cfrac { { \alpha }^{ 2 } }{ \beta } \right) }^{ \cfrac { 1 }{ 3 } }+{ \left( \cfrac { { \beta }^{ 2 } }{ \alpha } \right) }^{ \cfrac { 1 }{ 3 } }\Rightarrow \cfrac { { \alpha }^{ \cfrac { 2 }{ 3 } } }{ { \beta }^{ \cfrac { 1 }{ 3 } } } +\cfrac { { \beta }^{ \cfrac { 2 }{ 3 } } }{ { \alpha }^{ \cfrac { 1 }{ 3 } } } =\cfrac { \alpha +\beta }{ { \left( \alpha \beta \right) }^{ \cfrac { 1 }{ 3 } } } =\cfrac { \cfrac { 5 }{ 2 } }{ { (8) }^{ \cfrac { 1 }{ 3 } } } =\cfrac { 5 }{ 4 }$$Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More