TS EAMCET · Maths · Quadratic Equation
\(\alpha, \beta\) are the real roots of the equation \(12 x^{1 / 3}-25 x^{1 / 6}+12=0\). If \(\alpha\gt\beta\), then \(\sqrt[6]{\frac{\alpha}{\beta}}=\)
- A \(\frac{3}{2}\)
- B \(\frac{4}{3}\)
- C \(\frac{9}{8}\)
- D \(\frac{16}{9}\)
Answer & Solution
Correct Answer
(D) \(\frac{16}{9}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & 12 x^{\frac{1}{3}}-25 x^{\frac{1}{6}}+12=0 . \text { Let } x^{1 / 6}=t \\ & 12 t^2-25 t+12=0, \text { On solving, } t=\frac{4}{3}, \frac{3}{4} \\ & \alpha^{1 / 6}=\frac{4}{3} \beta^{1 / 6}=\frac{3}{4} \Rightarrow \alpha=\left(\frac{4}{3}\right)^6,…
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