JEE Main 2023MathematicsQuadratic EquationMediumNumerical

JEE Main 2023 — Quadratic Equation Question with Solution

JEE Main 2023 (11 Apr Shift 1)

Question

If a and b are the roots of the equation x2-7x-1=0, then the value of a21+b21+a17+b17a19+b19 is equal to

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Show full solutionCorrect answer: 51
Correct answer
51

Step-by-step explanation

Since, a and b are roots of x2-7x-1=0, so

a2-7a-1=0

⇒a2-1=7a

⇒a4+1-2a2=49a2

⇒a4+1=51a2   ...1

Similarly,

b4+1=51b2   ...2

Now,

a21+b21+a17+b17a19+b19

=a17a4+1+b17b4+1a19+b19

=51a19+51b19a19+b19

=51

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About this question

This is a previous-year question from JEE Main 2023, covering the Quadratic Equation chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.