What is the answer to A^2+A^{-1}=0 ?

The answer to A^2+A^{-1}=0 is A=-1,A= 1/2-(sqrt(3))/2 i,A= 1/2+(sqrt(3))/2 i

Solve for A: A^2+A^{-1}=0

The solution is A=-1,A= 1/2-(sqrt(3))/2 i,A= 1/2+(sqrt(3))/2 i

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A^{2} + A^{- 1} = 0

A = - 1, A = \frac{1}{2} - \frac{3}{2} i, A = \frac{1}{2} + \frac{3}{2} i

Solution steps

A^{2} + A^{- 1} = 0

Refine

A^{2} + \frac{1}{A} = 0

Multiply both sides by

A

A^{3} + 1 = 0

Solve

A^{3} + 1 = 0 : A = - 1, A = \frac{1}{2} - \frac{3}{2} i, A = \frac{1}{2} + \frac{3}{2} i

A = - 1, A = \frac{1}{2} - \frac{3}{2} i, A = \frac{1}{2} + \frac{3}{2} i

Verify Solutions

Find undefined (singularity) points:

A = 0

Combine undefined points with solutions:

A = - 1, A = \frac{1}{2} - \frac{3}{2} i, A = \frac{1}{2} + \frac{3}{2} i

b, a = \frac{2 a + 6 b}{3 b}

\frac{3 - 2}{9 b} = \frac{1}{3 b - 7}

\frac{2}{w} = \frac{7}{w + 5}

b, a = \frac{3 b - 1}{3 b - 4}

\frac{5}{x + 1} = 3 - \frac{x}{x + 1}

What is the answer to A^2+A^{-1}=0 ?
The answer to A^2+A^{-1}=0 is A=-1,A= 1/2-(sqrt(3))/2 i,A= 1/2+(sqrt(3))/2 i
Solve for A: A^2+A^{-1}=0
The solution is A=-1,A= 1/2-(sqrt(3))/2 i,A= 1/2+(sqrt(3))/2 i