Question
If $$x = \root 3 \of {2 + \sqrt 3 } {\text{,}}$$ then the value of $${x^3}{\text{ + }}\frac{1}{{{x^3}}}$$ is?
Answer: Option D
$$\eqalign{
& {\text{ }}x = \root 3 \of {2 + \sqrt 3 } \cr
& {x^3} = 2 + \sqrt 3 \cr
& \frac{1}{{{x^3}}} = \frac{1}{{2 + \sqrt 3 }} \times \frac{{2 - \sqrt 3 }}{{2 - \sqrt 3 }} = 2 - \sqrt 3 \cr
& \therefore {x^3}{\text{ + }}\frac{1}{{{x^3}}} \cr
& = 2 + \sqrt 3 + 2 - \sqrt 3 \cr
& = 4 \cr} $$
Was this answer helpful ?
$$\eqalign{
& {\text{ }}x = \root 3 \of {2 + \sqrt 3 } \cr
& {x^3} = 2 + \sqrt 3 \cr
& \frac{1}{{{x^3}}} = \frac{1}{{2 + \sqrt 3 }} \times \frac{{2 - \sqrt 3 }}{{2 - \sqrt 3 }} = 2 - \sqrt 3 \cr
& \therefore {x^3}{\text{ + }}\frac{1}{{{x^3}}} \cr
& = 2 + \sqrt 3 + 2 - \sqrt 3 \cr
& = 4 \cr} $$
Was this answer helpful ?
More Questions on This Topic :
Question 3. If **Hidden Equation** is?
Question 7. Simplified value of **Hidden Equation** = ?
Question 8. If **Hidden Equation**
Question 10. If **Hidden Equation** ....
Latest Videos
Latest Test Papers
Submit Solution