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

The answer to x^{-2}-2x^{-1}-1=0 is x=-1-sqrt(2),x=sqrt(2)-1

Solve for x: x^{-2}-2x^{-1}-1=0

The solution is x=-1-sqrt(2),x=sqrt(2)-1

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x^{- 2} - 2 x^{- 1} - 1 = 0

x = - 1 - 2, x = 2 - 1

Decimal Notation

x = - 2.41421 \dots, x = 0.41421 \dots

Solution steps

x^{- 2} - 2 x^{- 1} - 1 = 0

Refine

\frac{1}{x ^{2}} - \frac{2}{x} - 1 = 0

Multiply by LCM

1 - 2 x - x^{2} = 0

Solve

1 - 2 x - x^{2} = 0 : x = - 1 - 2, x = 2 - 1

x = - 1 - 2, x = 2 - 1

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - 1 - 2, x = 2 - 1

0 = \frac{9 - x ^{2}}{x ^{2} + 3 x}

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

x, \frac{x - 2}{x + 10} = 7

\frac{( 7500 - 100 p )}{100 p} = 0.3

x, 12 - \frac{1}{x} = x

What is the answer to x^{-2}-2x^{-1}-1=0 ?
The answer to x^{-2}-2x^{-1}-1=0 is x=-1-sqrt(2),x=sqrt(2)-1
Solve for x: x^{-2}-2x^{-1}-1=0
The solution is x=-1-sqrt(2),x=sqrt(2)-1