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$I f \sqrt{3} \sin π x + \cos π x = x^{2} - \frac{2}{3} x + \frac{19}{9}, t h e n x i s e q u a l t o$

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Correct option is B

We have 3sinπx+cosπx=x2−23x+199=x-132+2 Now -2≤3sinπx+cosπx≤2, i.e.,LHS≤2, and RHS≥2. ∴LHS=RHS=2 ⇒x=13

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If 3sinπx+cosπx=x2−23x+199, then x is equal to

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$I f \sqrt{3} \sin π x + \cos π x = x^{2} - \frac{2}{3} x + \frac{19}{9}, t h e n x i s e q u a l t o$