The solution set of the equation $$sin$$$$π$$$$x23=x2$$−$$23x+4$$

Correct option is 2is having only one element

Questions

The solution set of the equation
$\sin (\frac{π x}{2 \sqrt{3}}) = x^{2} - 2 \sqrt{3} x + 4$

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Forms an empty set

is having only one element

is having only two elements

is having greater than two elements

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detailed solution

Correct option is B

We have sinπx23=x2−23x+4.Since −1≤sinπx23≤1,⇒−1≤x2−23x+4≤1⇒ x2−23x+3≤0⇒ x−32≤0 But x−32≥0 ⇒x−32=0⇒ x=3

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The solution set of the equation sinπx23=x2−23x+4

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The solution set of the equation
$\sin (\frac{π x}{2 \sqrt{3}}) = x^{2} - 2 \sqrt{3} x + 4$