Jee mains pyq maths

Question

If the domain of the function \(f(x) = \frac{\sqrt{x^2 - 25}}{4 - x^2} + \log(x^2 + 2x - 15)\) is (–∞, α) ∪ [β, ∞), then α² + β² is equal to _____.

Answer 1

x² – 25 ≥ 0 

⇒ x ∈ (–∞, –5) ∪ [5, ∞)

4 – x² ≠ 0

⇒ x ≠ –2, 2

x² + 2x – 15 > 0

(x + 5) (x – 3) > 0

x ∈ (–∞, –5) ∪ (3, ∞)

So, x ∈ (–∞, –5) ∪ [5, ∞)

α = –5

β = 5

α² + β² = 50