Let S denotes the set of all real values of the parameter ‘a’ for which every solution of the inequality log1/2 x2 ≥ log1/2 (x + 2) is the solution of the inequality 49x2 – 4a4 ≤ 0. What is the value of S? ∪
Let S denotes the set of all real values of the parameter ‘a’ for which every solution of the inequality log1/2 x2 ≥ log1/2 (x + 2) is the solution of the inequality 49x2 – 4a4 ≤ 0. What is the value of S? ∪ Correct Answer (-∞, -√7
We have, log1/2 x2 ≥ log1/2 (x + 2) => x2 ≤ x + 2 => -1 ≤ x ≤ 2 And, 49x2 – 4a4 ≤ 0 i.e. x2 ≤ 4a4 / 49 => -2a2/7 ≤ a ≤ 2a2/7 From the above equations, -2a2/7 ≤ -1 and 2 ≤ 2a2/7 i.e. a2 € 7/2 and a2 ≥ 7 => a € (-∞, -√7] ∪ ∪ [√7, ∞)