The number of elements in the set S = x ∈ ℝ : 2 cos x 2 + x 6 = 4 x + 4 - x is

Step-by-step solution

Given, 2 cos x 2 + x 6 = 4 x + 4 - x Now we know that maximum value of cos function is 1 , so 2 cos x 2 + x 6 ≤ 2 and using A . M ≥ G . M we get 4 x + 4 - x ≥ 2 So, L . H . S . ≤ 2 .   &   R . H . s   ≥ 2 Hence L . H . S . = 2   &   R . H . S . = 2 Now equating both to 2 we get, 2 cos x 2 + x 6 = 2 and 4 x + 4 - x = 2 Now solving 2 cos x 2 + x 6 = 2 ⇒ cos x 2 + x 6 = 1 ⇒ x 2 + x 6 = 0 ⇒ x 2 + x = 0 ⇒ x = 0   or   - 1 &#