If α and β are the roots of the equation 8x 2 - 3x + 27 = 0, find the value of (α 2/β) 1/3 + (β 2/α) 1/3

Since, α and β are the roots of the equation
8x² - 3x + 27 = 0
∴ α + β = 3/8 and α β = 27/8
∴ (α²/β)^1/3 + (β²/α )^1/8
= (α³)^1/3 + (β³)^1/3/(αβ)³
= α + β / (αβ)^1/3 = 3/8/(27/8)^1/3
= 3/8 x 2/3 = 1/4