JEE Main 2024 Mathematics question
Let a, b, c be the lengths of three sides of a triangle satisfying the condition (a² + b²)x² − 2b(a + c)x + (b² + c²) = 0. If the set of all possible values of x is the interval (α, β), then 12(α² + β²) is equal to .
Answer: 36
Solution
The equation can be written as (ax − b)² + (bx − c)² = 0, so ax = b and bx = c, i.e. b² = ac and x = b/a = c/b. The triangle inequalities a + b > c, b + c > a and c + a > b
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