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

LHS=3sinπx+cosπx≤2 and RHS = x2−23x+199=x-132+2≥2∴LHS=RHS=2⇒x=13

LHS=3sinπx+cosπx≤2 and RHS = x2−23x+199=x-132+2≥2∴LHS=RHS=2⇒x=13

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If $\sqrt{3} \sin π x + \cos π x = x^{2} - \frac{2}{3} x + \frac{19}{9}$ , then x is equal to

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$- \frac{1}{3}$

$\frac{2}{3}$

$\frac{4}{3}$

$\frac{1}{3}$

answer is B.

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LHS $= \sqrt{3} \sin π x + \cos π x \leq 2$ and RHS = $x^{2} - \frac{2}{3} x + \frac{19}{9} = {(x - \frac{1}{3})}^{2} + 2 \geq 2$

$∴ L H S = R H S = 2 \Rightarrow x = \frac{1}{3}$

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