The equation has real solution if

Maths Quadratic Equations Solution of Quadratic Inequations and Miscellaneous Equations Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(b, d)

(sin 2 x) 3 + (cos 2 x) 3 = a 2

⇒ (sin 4 x – sin 2 x cos 2 x + cos 4 x) = a 2 ⇒ (sin

2 x + cos 2 x) 2 –3sin 2 x cos 2 x = a 2 ⇒ 3 sin

2 x cos 2 x = 1 – a 2

⇒ (sin 2 2x) = 1 – a 2

⇒ (1 – a 2 ) = sin 2 2x

but 0 ≤ sin 2 2x ≤ 1

⇒ 0 ≤ (1 – a 2 ) ≤ 1

⇒ ≤ a 2 ≤ 1

⇒ a ∈ [–1, –1/2] ∪ [1/2, 1]

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