JEE Main 2024 Mathematics question
Let a > 0 be a root of the equation 2x² + x − 2 = 0. If , where α, β ∈ Z then α + β is equal to .
Answer: 170
Solution
The roots of 2x² + x − 2 are a and b with ab = −1, so 1/a and 1/b are the roots of 2x² − x − 2 and 2 + x − 2x² = −2(x − 1/a)(x − 1/b). Near x = 1/a, 1 − cos u ≈
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