Atrast α (complex solution)
\alpha =\beta +\frac{i\sqrt{2x-10}}{2x}
\alpha =\beta -\frac{i\sqrt{2x-10}}{2x}\text{, }x\neq 0
Atrast x
\left\{\begin{matrix}x=\frac{\sqrt{40\alpha ^{2}-80\alpha \beta +40\beta ^{2}+1}-1}{4\left(\alpha -\beta \right)^{2}}\text{; }x=-\frac{\sqrt{40\alpha ^{2}-80\alpha \beta +40\beta ^{2}+1}+1}{4\left(\alpha -\beta \right)^{2}}\text{, }&\alpha \neq \beta \\x=5\text{, }&\alpha =\beta \end{matrix}\right,
Atrast α
\alpha =\beta -\frac{\sqrt{10-2x}}{2|x|}
\alpha =\beta +\frac{\sqrt{10-2x}}{2|x|}\text{, }x\neq 0\text{ and }x\leq 5
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