\left\{ \begin{array} { l } { a c = \frac { 16 } { 3 } } \\ { a ^ { 2 } + c ^ { 2 } = \frac { 43 } { 3 } } \end{array} \right.
Solve for a, c
a=-\frac{\sqrt{33}}{6}-\frac{5}{2}\approx -3.457427108\text{, }c=\frac{\sqrt{33}}{6}-\frac{5}{2}\approx -1.542572892
a=\frac{\sqrt{33}}{6}+\frac{5}{2}\approx 3.457427108\text{, }c=-\frac{\sqrt{33}}{6}+\frac{5}{2}\approx 1.542572892
a=\frac{\sqrt{33}}{6}-\frac{5}{2}\approx -1.542572892\text{, }c=-\frac{\sqrt{33}}{6}-\frac{5}{2}\approx -3.457427108
a=-\frac{\sqrt{33}}{6}+\frac{5}{2}\approx 1.542572892\text{, }c=\frac{\sqrt{33}}{6}+\frac{5}{2}\approx 3.457427108
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