Mathematics - Functions Question with Solution | TestHub

The equation for $x$ is given by:

$$x=\frac{5\pm \sqrt{25+4\sin x-24}}{2}$$

This simplifies to:

$$x=\frac{5\pm \sqrt{1+4\sin x}}{2}$$

Considering the range of $\sin x$:

$$-1\le \sin x\le 1$$

Multiplying by 4:

$$-4\le 4\sin x\le 4$$

Adding 1:

$$-3\le 1+4\sin x\le 5$$

For the square root to be real, $1+4\sin x\ge 0$, so:

$$0\le 1+4\sin x\le 5$$

If $x$ is an integer, then $\sin x=0$.

This implies $x=3$.

Therefore, $x=\pi$.