Riješi y=sqrt{2x+1/(x-3)(5-x)}

$$y = \sqrt { \frac { 2 x + 1 } { ( x - 3 ) ( 5 - x ) } }$$

Izračunaj x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{y^{4}-9y^{2}+1}+4y^{2}-1}{y^{2}}\text{; }x=\frac{-\sqrt{y^{4}-9y^{2}+1}+4y^{2}-1}{y^{2}}\text{, }&arg(y)<\pi \text{ and }y\neq 0\\x=-\frac{1}{2}=-0,5\text{, }&y=0\end{matrix}\right,$$

Izračunaj y (complex solution)

$$y=\sqrt{\frac{2x+1}{\left(5-x\right)\left(x-3\right)}}$$

$$x\neq 3\text{ and }x\neq 5$$

Izračunaj x

$$\left\{\begin{matrix}x=\frac{\sqrt{y^{4}-9y^{2}+1}+4y^{2}-1}{y^{2}}\text{; }x=\frac{-\sqrt{y^{4}-9y^{2}+1}+4y^{2}-1}{y^{2}}\text{, }&\left(y>0\text{ and }y\leq \frac{\sqrt{11}-\sqrt{7}}{2}\right)\text{ or }y\geq \frac{\sqrt{7}+\sqrt{11}}{2}\\x=-\frac{1}{2}=-0,5\text{, }&y=0\end{matrix}\right,$$

Izračunaj y

$$y=\sqrt{\frac{2x+1}{\left(5-x\right)\left(x-3\right)}}$$

$$\left(x>3\text{ and }x<5\right)\text{ or }x\leq -\frac{1}{2}$$