Solve {l}{a_{4}+a_{5}+a_{6}+a_{7}=20}{a_{4}a_{7}=16}

$$\left. \begin{array} { l } { a _ { 4 } + a _ { 5 } + a _ { 6 } + a _ { 7 } = 20 } \\ { a _ { 4 } a _ { 7 } = 16 } \end{array} \right.$$

Solve for a_4, a_5, a_6, a_7 (complex solution)

$$a_{4}=\frac{\sqrt{\left(a_{5}+a_{6}-28\right)\left(a_{5}+a_{6}-12\right)}-a_{5}-a_{6}+20}{2}\text{, }a_{5}\in \mathrm{C}\text{, }a_{6}\in \mathrm{C}\text{, }a_{7}=\frac{-\sqrt{\left(a_{5}+a_{6}-28\right)\left(a_{5}+a_{6}-12\right)}-a_{5}-a_{6}+20}{2}$$

$$a_{4}=\frac{-\sqrt{\left(a_{5}+a_{6}-28\right)\left(a_{5}+a_{6}-12\right)}-a_{5}-a_{6}+20}{2}\text{, }a_{5}\in \mathrm{C}\text{, }a_{6}\in \mathrm{C}\text{, }a_{7}=\frac{\sqrt{\left(a_{5}+a_{6}-28\right)\left(a_{5}+a_{6}-12\right)}-a_{5}-a_{6}+20}{2}$$

Solve for a_4, a_5, a_6, a_7

$$a_{4}=\frac{\sqrt{(a_{5}+a_{6}-28)(a_{5}+a_{6}-12)}-a_{5}-a_{6}+20}{2}\text{, }a_{5}\in (-\infty,12-a_{6}]\cup [28-a_{6},\infty)\text{, }a_{6}\in \mathrm{R}\text{, }a_{7}=\frac{-\sqrt{(a_{5}+a_{6}-28)(a_{5}+a_{6}-12)}-a_{5}-a_{6}+20}{2}\text{; }a_{4}=\frac{-\sqrt{(a_{5}+a_{6}-28)(a_{5}+a_{6}-12)}-a_{5}-a_{6}+20}{2}\text{, }a_{5}\in (-\infty,12-a_{6}]\cup [28-a_{6},\infty)\text{, }a_{6}\in \mathrm{R}\text{, }a_{7}=\frac{\sqrt{(a_{5}+a_{6}-28)(a_{5}+a_{6}-12)}-a_{5}-a_{6}+20}{2}$$