What is the answer to x+x^{-1}=4 ?

The answer to x+x^{-1}=4 is x=2+sqrt(3),x=2-sqrt(3)

Solve for x: x+x^{-1}=4

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

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x + x^{- 1} = 4

x = 2 + 3, x = 2 - 3

Decimal Notation

x = 3.73205 \dots, x = 0.26794 \dots

Solution steps

x + x^{- 1} = 4

Refine

x + \frac{1}{x} = 4

Multiply both sides by

x

x^{2} + 1 = 4 x

Solve

x^{2} + 1 = 4 x : x = 2 + 3, x = 2 - 3

x = 2 + 3, x = 2 - 3

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 2 + 3, x = 2 - 3

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

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

F = G \frac{mm}{d ^{2}}

\frac{w + 3}{4 w} + 1 = \frac{w - 5}{w}

y, x = 4 y + \frac{1}{y}

What is the answer to x+x^{-1}=4 ?
The answer to x+x^{-1}=4 is x=2+sqrt(3),x=2-sqrt(3)
Solve for x: x+x^{-1}=4
The solution is x=2+sqrt(3),x=2-sqrt(3)