What is the answer to x+x^{-1}=3 ?

The answer to x+x^{-1}=3 is x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2

Solve for x: x+x^{-1}=3

The solution is x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2

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x + x^{- 1} = 3

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

Decimal Notation

x = 2.61803 \dots, x = 0.38196 \dots

Solution steps

x + x^{- 1} = 3

Refine

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

Multiply both sides by

x

x^{2} + 1 = 3 x

Solve

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

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

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

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

\frac{5}{x + 2} + \frac{3}{x - 4} = 2

l, E = \frac{a - r l}{l - r}

\frac{1}{n - 8} - 1 = \frac{7}{n - 8}

\frac{1}{x - 2} + 5 = \frac{16}{x - 2}

t, m - 5 n = \frac{f}{t}

What is the answer to x+x^{-1}=3 ?
The answer to x+x^{-1}=3 is x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2
Solve for x: x+x^{-1}=3
The solution is x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2