Question

If a, b are the roots of the equation 8x² –3x + 27 = 0, then the value of $\left( \frac{\alpha^{2}}{\beta} \right)^{1/3}$+ $\left( \frac{\beta^{2}}{\alpha} \right)^{1/3}$is-

• A. 1/3
• B. ј
• C. 7/2
• D. 4

Answer 1

Answer: (B)

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Answer 2

If a, b are roots of 8x² –3x + 27 = 0

a + b = $\frac{3}{8}$, ab = $\frac{27}{8}$

$\left( \frac{\alpha^{2}}{\beta} \right)^{1/3}$+ $\left( \frac{\beta^{2}}{\alpha} \right)^{1/3}$= $\frac{(\alpha^{3})^{1/3} + (\beta^{3})^{1/3}}{(\alpha\beta)^{1/3}}$= $\frac{\alpha + \beta}{(\alpha\beta)^{1/3}}$

= $\frac{3/8}{\left( \frac{27}{8} \right)^{1/3}}$= $\frac{1}{4}$