求解 {l}{ygeqx^2+3x-2}{ygeqx+3}

$$\left. \begin{array} { l } { y \geq x ^ { 2 } + 3 x - 2 } \\ { y \geq x + 3 } \end{array} \right.$$

求解 x 的值

$$\left\{\begin{matrix}x=-\frac{3}{2}=-1.5\text{, }&y\geq \frac{3}{2}\\x\in \begin{bmatrix}\frac{-\sqrt{4y+17}-3}{2},\frac{\sqrt{4y+17}-3}{2}\end{bmatrix}\text{, }&y\geq \sqrt{6}+2\\x=y-3\text{, }&y=2-\sqrt{6}\\x\in \begin{bmatrix}\frac{-\sqrt{4y+17}-3}{2},y-3\end{bmatrix}\text{, }&y>2-\sqrt{6}\text{ and }y<\sqrt{6}+2\end{matrix}\right.$$

求解 y 的值

$$\left\{\begin{matrix}y\geq x+3\text{, }&x\geq -\sqrt{6}-1\text{ and }x\leq \sqrt{6}-1\\y\geq x^{2}+3x-2\text{, }&x<-\sqrt{6}-1\text{ or }x>\sqrt{6}-1\end{matrix}\right.$$