Solve x^2-alphax+1=0

$$x ^ { 2 } - \alpha x + 1 = 0$$

Solve for α

$$\alpha =x+\frac{1}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-\alpha x+1=-x^{2}$$

Subtract 1 from both sides.

$$-\alpha x=-x^{2}-1$$

The equation is in standard form.

$$\left(-x\right)\alpha =-x^{2}-1$$

Divide both sides by -x.

$$\frac{\left(-x\right)\alpha }{-x}=\frac{-x^{2}-1}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$\alpha =\frac{-x^{2}-1}{-x}$$

Divide -x^{2}-1 by -x.

$$\alpha =x+\frac{1}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{\alpha ^{2}-4}+\alpha }{2}$$

$$x=\frac{-\sqrt{\alpha ^{2}-4}+\alpha }{2}$$

Solve for x

$$x=\frac{\sqrt{\alpha ^{2}-4}+\alpha }{2}$$

$$x=\frac{-\sqrt{\alpha ^{2}-4}+\alpha }{2}\text{, }|\alpha |\geq 2$$