Multiple choice

If $ \alpha, \beta $ are the roots of the equation $ 8x^2-3x+27=0 $, then the value of $\left( \dfrac { \alpha ^{ 2 } }{ \beta } \right) ^{ \frac { 1 }{ 3 } }+\left( \dfrac { \beta ^{ 2 } }{ \alpha } \right) ^{ \frac { 1 }{ 3 } }$ is

  1. $ \dfrac{1}{3} $
  2. $ \dfrac{1}{4} $
  3. $ \dfrac{7}{2} $
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 8x^2 - 3x + 27 = 0, alpha + beta = 3/8 and alpha * beta = 27/8. The expression is (alpha^2/beta)^(1/3) + (beta^2/alpha)^(1/3) = (alpha + beta) / (alpha * beta)^(1/3). This simplifies to (3/8) / (27/8)^(1/3) = (3/8) / (3/2) = 3/8 * 2/3 = 1/4.

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