\left\{ \begin{array} { l } { M ^ { 2 } \times N ^ { 2 } = \frac { 5 } { 4 } } \\ { 10 + 3 M + 2 N - \frac { 5 } { 2 } = 0 } \end{array} \right.
Solve for M, N
M=-\frac{\sqrt{48\sqrt{5}+225}}{12}-\frac{5}{4}\approx -2.769162925\text{, }N=\frac{\sqrt{48\sqrt{5}+225}-15}{8}\approx 0.403744387
M=-\frac{\sqrt{225-48\sqrt{5}}}{12}-\frac{5}{4}\approx -2.15396018\text{, }N=\frac{\sqrt{225-48\sqrt{5}}-15}{8}\approx -0.51905973
M=\frac{\sqrt{225-48\sqrt{5}}}{12}-\frac{5}{4}\approx -0.34603982\text{, }N=\frac{-\sqrt{225-48\sqrt{5}}-15}{8}\approx -3.23094027
M=\frac{\sqrt{48\sqrt{5}+225}}{12}-\frac{5}{4}\approx 0.269162925\text{, }N=\frac{-\sqrt{48\sqrt{5}+225}-15}{8}\approx -4.153744387
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