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

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

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

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

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

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

Decimal

x = 1.61803 \dots, x = - 0.61803 \dots

Solution steps

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

Refine

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

Multiply by LCM

x + 1 = x^{2}

Solve

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

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

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

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

- \frac{6}{7} - \frac{1}{x + 5} = \frac{2}{x + 5}

6 = \frac{3}{2 x}

\frac{1}{x + 5} + \frac{10}{x ^{2} - 25} = 1

7 - \frac{2}{x - 4} = x

\frac{5 a}{a + 2} = 0

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