解決(alpha-beta)^2quad2x^2+x-5=0 |Microsoft數學求解器

$$( \alpha - \beta ) ^ { 2 } \quad 2 x ^ { 2 } + x - 5 = 0$$

解 α (復數求解)

$$\alpha =\beta +\frac{i\sqrt{2x-10}}{2x}$$

$$\alpha =\beta -\frac{i\sqrt{2x-10}}{2x}\text{, }x\neq 0$$

解 x

$$\left\{\begin{matrix}x=\frac{\sqrt{40\alpha ^{2}-80\alpha \beta +40\beta ^{2}+1}-1}{4\left(\alpha -\beta \right)^{2}}\text{; }x=-\frac{\sqrt{40\alpha ^{2}-80\alpha \beta +40\beta ^{2}+1}+1}{4\left(\alpha -\beta \right)^{2}}\text{, }&\alpha \neq \beta \\x=5\text{, }&\alpha =\beta \end{matrix}\right.$$

解 α

$$\alpha =\beta -\frac{\sqrt{10-2x}}{2|x|}$$

$$\alpha =\beta +\frac{\sqrt{10-2x}}{2|x|}\text{, }x\neq 0\text{ and }x\leq 5$$