Question

If √3 sinπx + cosπx = x² - 2/3x + 19/9, then x is equal to

(a)  -1/3

(b)  1/3

(c)  2/3

(d)  None of these

Answer 1

Correct option (b)  1/3

So equality holds for x = 1/3.

RHS = x² - 2/3x + 19/9 = (x - 1/3)² + 2 ≥ 2

So equality holds if x = 1/3.

Thus, LHS = RHS for x = 1/3 only.