If α, β are the roots of the equation x²-(5+3^(√(log ₃ 5))-5^(√(log ₅ 3)))x+3(3^(log ₃ 5)^(1/3)-5^(log ₅ 3)^(2/3)-1)=0, then the equation, whose roots are α+1/(β) and β+1/(α), is:

Complex Numbers and Quadratic Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 27 Jul, Evening shift · Q5157

JEE Main 202227 Jul, Evening shiftMathematicsHardComplex Numbers and Quadratic Equations264× since 2002

\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}

and

\beta+\frac{1}{\alpha}

, is :

JEE Main 2022 · 27 Jul, Evening shift · Q5157

JEE Main 202227 Jul, Evening shiftMathematicsHardComplex Numbers and Quadratic Equations264× since 2002

\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}

and

\beta+\frac{1}{\alpha}

, is :