If - - are the roots of the equation 8 x 2-3 x -27-0- then the value of a 2-1-3-2-1-3A- 7-2B- 1-3C- 1-4D- 4

The correct option is C α + β = 3/8, αβ = 27/8 ∴ ( α^2/β )^1/3 + ( β^2/α )^1/3 = (α^3)^1/3 + (β^3)^1/3/(αβ)^1/3 = α + β/(αβ)^1/3=3/8/(27/8)^1/3=3/8/3/2 = 1/ ...

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Byju's Answer

Standard X

Mathematics

Sum and Product of Roots of a Quadratic Equation

If α, β are t...

Question

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

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Solution

The correct option is B

$α + β = \frac{3}{8}, α β = \frac{27}{8} ∴ {(\frac{α^{2}}{β})}^{\frac{1}{3}} + {(\frac{β^{2}}{α})}^{\frac{1}{3}} = \frac{(α^{3})^{\frac{1}{3}} + (β^{3})^{\frac{1}{3}}}{(α β)^{\frac{1}{3}}} = \frac{α + β}{(α β)^{\frac{1}{3}}} = \frac{3 / 8}{(27 / 8)^{\frac{1}{3}}} = \frac{3 / 8}{3 / 2} = \frac{1}{4}$ .

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If α,β are the roots of the equation 8x2−3x+27=0, then the value of (α2β)13+(β2α)13 is

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