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Q.
The number of solutions of the equation $\sin\left(\frac{\pi\,x}{2\sqrt{3}}\right)=x^2-2\sqrt{3}x+4$
Trigonometric Functions
Solution:
Since $\,\sin\,\left(\frac{\pi\,x}{2\sqrt{3}}\right) \le1$
$\therefore \, \, \,x^2-2\sqrt{3\,x}+4\,\leq\,1\Rightarrow x^2-2\sqrt{3x}+3\leq\,0$
$\Rightarrow (x-\sqrt{3})^2\,\leq\,0$
$\Rightarrow \, \, \, \,x=\sqrt{3}$ which gives the only solution,