What is the answer to x^2-2x= 1/x-2 ?

The answer to x^2-2x= 1/x-2 is x=1,x= 1/2+i(sqrt(3))/2 ,x= 1/2-i(sqrt(3))/2

Solve for x: x^2-2x= 1/x-2

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

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

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

Solution steps

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

Multiply both sides by

x

x^{3} - 2 x^{2} = 1 - 2 x

Solve

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

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

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

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

\frac{- 6}{m - 5} = \frac{- 2}{m + 3}

\frac{2}{x + 2} + 4 = \frac{14}{x + 2}

\frac{3 x}{x + 2} = \frac{3 x - 2}{x}

\frac{x - 2}{6 x} = \frac{x + 3}{5 x}

\frac{2}{x} = \frac{2 x}{1 + x ^{2}}

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