Solve {l}{a_{1}+a_{2}+a_{3}=34}{a_{2}*a_{3}=28}

$$\left. \begin{array} { l } { a _ { 1 } + a _ { 2 } + a _ { 3 } = 34 } \\ { a _ { 2 } \cdot a _ { 3 } = 28 } \end{array} \right.$$

Solve for a_1, a_2, a_3 (complex solution)

$$a_{1}\in \mathrm{C}\text{, }a_{2}=\frac{28}{a_{3}}\text{, }a_{3}=-\frac{\sqrt{a_{1}^{2}-68a_{1}+1044}}{2}-\frac{a_{1}}{2}+17$$

$$a_{1}\in \mathrm{C}\text{, }a_{2}=\frac{28}{a_{3}}\text{, }a_{3}=\frac{\sqrt{a_{1}^{2}-68a_{1}+1044}}{2}-\frac{a_{1}}{2}+17$$

Solve for a_1, a_2, a_3

$$a_{1}\in (-\infty,34-4\sqrt{7}]\cup [4\sqrt{7}+34,\infty)\text{, }a_{2}=\frac{28}{a_{3}}\text{, }a_{3}=\frac{\sqrt{a_{1}^{2}-68a_{1}+1044}}{2}-\frac{a_{1}}{2}+17\text{; }a_{1}\in (-\infty,34-4\sqrt{7}]\cup [4\sqrt{7}+34,\infty)\text{, }a_{2}=\frac{28}{a_{3}}\text{, }a_{3}=-\frac{\sqrt{a_{1}^{2}-68a_{1}+1044}}{2}-\frac{a_{1}}{2}+17$$