Selesaikan y=sqrt{x-3}+3sqrt{12-x}

$$y = \sqrt { x - 3 } + 3 \sqrt { 12 - x }$$

Cari nilai x (complex solution)

$$\left\{\begin{matrix}x=3\text{; }x=12\text{, }&|-arg(-y)+\pi |<\pi \\x=\frac{3\sqrt{90y^{2}-y^{4}}}{50}-\frac{2y^{2}}{25}+\frac{111}{10}\text{, }&|-arg(-y)+arg(-\sqrt{x-3}-3\sqrt{12-x})|<\pi \text{ and }|arg(\sqrt{-\frac{3\sqrt{90y^{2}-y^{4}}}{50}+\frac{2y^{2}}{25}+\frac{9}{10}}\sqrt{\frac{3\sqrt{90y^{2}-y^{4}}}{50}-\frac{2y^{2}}{25}+\frac{81}{10}})-arg(\frac{6\sqrt{90y^{2}-y^{4}}}{25}+\frac{9y^{2}}{50}-\frac{81}{10})|<\pi \text{ and }y\neq -3\text{ and }y\neq 3\\x=-\frac{3\sqrt{90y^{2}-y^{4}}}{50}-\frac{2y^{2}}{25}+\frac{111}{10}\text{, }&|-arg(-y)+arg(-\sqrt{x-3}-3\sqrt{12-x})|<\pi \text{ and }|arg(\sqrt{-\frac{3\sqrt{90y^{2}-y^{4}}}{50}-\frac{2y^{2}}{25}+\frac{81}{10}}\sqrt{\frac{3\sqrt{90y^{2}-y^{4}}}{50}+\frac{2y^{2}}{25}+\frac{9}{10}})-arg(-\frac{6\sqrt{90y^{2}-y^{4}}}{25}+\frac{9y^{2}}{50}-\frac{81}{10})|<\pi \text{ and }y\neq -9\text{ and }y\neq 9\end{matrix}\right,$$

Cari nilai y

$$y=\sqrt{x-3}+3\sqrt{12-x}$$

$$x\geq 3\text{ and }x\leq 12$$