Solve x^2-kx+1=0

$${ x }^{ 2 } -kx+1=0$$

Solve for k

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$-kx+1=-x^{2}$$

Subtract 1 from both sides.

$$-kx=-x^{2}-1$$

The equation is in standard form.

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

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

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

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

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

Solve for x (complex solution)

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

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

Solve for x

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

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