Question

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

Answer 1

$\frac{\pi x}{2\sqrt{3}}=x^2-2\sqrt{3}x+4$

$\pi z=2\sqrt{3}{x}^2-12x+8\sqrt{3}$

$2\sqrt{3}{x}^2-(\pi +12)x+8\sqrt{3}=0$

$x=\frac{\pi +12\pm \sqrt{(\pi +12{)}^2-4(2\sqrt{3}\left)\right(8\sqrt{3})}}{4\sqrt{3}}$

$x=\frac{\pi +12\pm \sqrt{{\pi }^2+24\pi +144-192}}{4\sqrt{3}}$

$x=\frac{\pi +12\pm \sqrt{{\pi }^2+24\pi +48}}{4\sqrt{3}}$

No. of solutions is two.