JEE Main 2024 Mathematics question
If α satisfies the equation x² + x + 1 = 0 and (1 + α)⁷ = A + Bα + Cα², A, B, C ≥ 0 then 5(3A – 2B – C) is equal to .
Answer: 5
Solution
α = ω or ω². For α = ω: (1 + ω)⁷ = (−ω²)⁷ = −ω¹⁴ = −ω² = 1 + ω. So A = 1, B = 1, C = 0, and 5(3A − 2B − C) = 5(3 − 2 − 0) = 5.