JEE Main 2024 Mathematics question
Let α, β be the roots of the equation x² – √6x + 3 = 0 such that Im(α) > Im(β). Let a, b be integers not divisible by 3 and n be a natural number such that , i = √−1. Then n + a + b is equal to .
Answer: 49
Solution
α = (√6/2)(1 + i) and β = (√6/2)(1 − i), with α + β = √6 and αβ = 3. Then α⁹⁹/β + α⁹⁸ = α⁹⁹(1/β + 1/α) = α⁹⁹(α + β)/(αβ) = α⁹⁹√6/3. Using α = √3 :
See the full step-by-step solution
Create a free account to read the complete working, and practise questions like this in a timed test.
Create a free account