Question

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 1

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, ∞)