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

JEE Main 2022 Mathematics question

If , are the roots of the equation : , then the equation, whose roots are and , is

(1)
(2)Correct
(3)
(4)

Answer: (2)

Solution

Using the identities and (each pair of terms is equal), the middle bracket reduces to 5 and the constant term to 3(0 − 1) = −3, so the equation becomes . Then and

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Question ID VK-034328