Question

The number of solutions of the equation $\sin \left(\frac{\pi x}{2\sqrt{3}}\right)=x^2-2\sqrt{3}x+4$

• A. form an empty set
• B. 1
• C. 2
• D. >2

Answer 1

Answer: (B)

Since $\sin \left(\frac{\pi x}{2\sqrt{3}}\right)\le 1$
$\therefore x^2-2\sqrt{3x}+4\le 1\Rightarrow x^2-2\sqrt{3x}+3\le 0$
$\Rightarrow (x-\sqrt{3}{)}^2\le 0$
$\Rightarrow x=\sqrt{3}$ which gives the only solution,