$$\left. \begin{array} { l } { a - b = 5 , a ^ { 2 } + b ^ { 2 } = 49 , } \\ { x + \frac { 1 } { x } = 5 , x ^ { 4 } + \frac { 1 } { x \right.$$
$x=\frac{5-\sqrt{21}}{2}\approx 0.208712153\text{, }a=\frac{5-\sqrt{73}}{2}\approx -1.772001873\text{, }b=\frac{-\sqrt{73}-5}{2}\approx -6.772001873$
$x=\frac{\sqrt{21}+5}{2}\approx 4.791287847\text{, }a=\frac{5-\sqrt{73}}{2}\approx -1.772001873\text{, }b=\frac{-\sqrt{73}-5}{2}\approx -6.772001873$
$x=\frac{5-\sqrt{21}}{2}\approx 0.208712153\text{, }a=\frac{\sqrt{73}+5}{2}\approx 6.772001873\text{, }b=\frac{\sqrt{73}-5}{2}\approx 1.772001873$
$x=\frac{\sqrt{21}+5}{2}\approx 4.791287847\text{, }a=\frac{\sqrt{73}+5}{2}\approx 6.772001873\text{, }b=\frac{\sqrt{73}-5}{2}\approx 1.772001873$
