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If α and β are the roots of the equation 8x2 - 3x + 27 = 0, find the value of (α2/β)1/3 + (β2/α)1/3
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- 1/3
- 1/4
- 7/2
- 4
- 9/2
Correct Option: B
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
