JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(\alpha, \beta\) are the roots of the equation \(x^{2}-\left(5+3 \sqrt{\log _{3} 5}-5 \sqrt{\log _{5} 3}\right)x+3\left(3^{\left(\log _{3} 5\right)^{\frac{1}{3}}}-5^{\left(\log _{5} 3\right)^{\frac{2}{3}}}-1\right)=0\) then the equation, whose roots are \(\alpha+\frac{1}{\beta} \text { and } \beta+\frac{1}{\alpha} \text {, }\)
- A \(3 x^{2}-20 x-12=0\)
- B \(3 x^{2}-20 x+16=0\)
- C \(3 x ^{2}-10 x +2=0\)
- D \(3 x^{2}-10 x-4=0\)
Answer & Solution
Correct Answer
(D) \(3 x^{2}-10 x-4=0\)
Step-by-step Solution
Detailed explanation
Bonus because ' \(x\) ' is missing the correct will be, \(x^{2}-\left(5+3 \sqrt{\sqrt{\log _{3} 5}}-5 \sqrt{\log _{5} 3}\right) x+3\left(3^{\left(\log _{3} 5\right)^{\frac{1}{3}}}-5^{\left(\log _{5} 3\right)^{\frac{2}{3}}}-1\right)=0\)…
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