Let S denotes the set of all real values of the parameter ‘a’ for which every solution of the inequality log1/2 x^2 ≥ log1/2 (x + 2) is the solution of the inequality 49x^2 – 4a^4 ≤ 0. What is the value of S?(a) (-∞, -√7) ∪ (√7, ∞)(b) (-∞, -√7] ∪ [√7, ∞)(c) (-√7, √7)(d) [-√7, √7]The question was asked during a job interview.I want to ask this question from Applications of Quadratic Equations topic in section Complex Numbers and Quadratic Equations of Mathematics – Class 11

Let S denotes the set of all real values of the parameter ‘a’ for

1.	Let S denotes the set of all real values of the parameter ‘a’ for which every solution of the inequality log1/2 x^2 ≥ log1/2 (x + 2) is the solution of the inequality 49x^2 – 4a^4 ≤ 0. What is the value of S?(a) (-∞, -√7) ∪ (√7, ∞)(b) (-∞, -√7] ∪ [√7, ∞)(c) (-√7, √7)(d) [-√7, √7]The question was asked during a job interview.I want to ask this question from Applications of Quadratic Equations topic in section Complex Numbers and Quadratic Equations of Mathematics – Class 11
Answer» The correct choice is (B) (-∞, -√7] ∪ [√7, ∞) Best explanation: We have, log1/2 x^2 ≥ log1/2 (x + 2) => x^2 ≤ x + 2 => -1 ≤ x ≤ 2 And, 49x^2 – 4a^4 ≤ 0 i.e. x^2 ≤ 4a^4 / 49 => -2a^2/7 ≤ a ≤ 2a^2/7 From the above EQUATIONS, -2a^2/7 ≤ -1 and 2 ≤ 2a^2/7 i.e. a^2 €7/2 and a^2 ≥ 7 => a € (-∞, -√7] ∪ [√7, ∞) So, S = (-∞, -√7] ∪ [√7, ∞)

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