What is the answer to -z+z^{-2}=2 ?

The answer to -z+z^{-2}=2 is z=-1,z=(-1+sqrt(5))/2 ,z=(-1-sqrt(5))/2

Solve for z: -z+z^{-2}=2

The solution is z=-1,z=(-1+sqrt(5))/2 ,z=(-1-sqrt(5))/2

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- z + z^{- 2} = 2

z = - 1, z = \frac{- 1 + 5}{2}, z = \frac{- 1 - 5}{2}

Decimal Notation

z = - 1, z = 0.61803 \dots, z = - 1.61803 \dots

Solution steps

- z + z^{- 2} = 2

Refine

- z + \frac{1}{z ^{2}} = 2

Multiply both sides by

z^{2}

- z^{3} + 1 = 2 z^{2}

Solve

- z^{3} + 1 = 2 z^{2} : z = - 1, z = \frac{- 1 + 5}{2}, z = \frac{- 1 - 5}{2}

z = - 1, z = \frac{- 1 + 5}{2}, z = \frac{- 1 - 5}{2}

Verify Solutions

Find undefined (singularity) points:

z = 0

Combine undefined points with solutions:

z = - 1, z = \frac{- 1 + 5}{2}, z = \frac{- 1 - 5}{2}

\frac{y - 1}{y - 3} = \frac{2}{y - 3}

x + \frac{10}{x} = - 7

\frac{6}{x ^{2} - 9} - \frac{1}{x - 3} = 1

\frac{x - 3}{x} = \frac{- 8}{x + 3}

14 = \frac{7 x}{9 + 4 x}

What is the answer to -z+z^{-2}=2 ?
The answer to -z+z^{-2}=2 is z=-1,z=(-1+sqrt(5))/2 ,z=(-1-sqrt(5))/2
Solve for z: -z+z^{-2}=2
The solution is z=-1,z=(-1+sqrt(5))/2 ,z=(-1-sqrt(5))/2