What is the answer to w+w^{-1}=13 ?

The answer to w+w^{-1}=13 is w=(13+sqrt(165))/2 ,w=(13-sqrt(165))/2

Solve for w: w+w^{-1}=13

The solution is w=(13+sqrt(165))/2 ,w=(13-sqrt(165))/2

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w + w^{- 1} = 13

w = \frac{13 + 165}{2}, w = \frac{13 - 165}{2}

Decimal Notation

w = 12.92261 \dots, w = 0.07738 \dots

Solution steps

w + w^{- 1} = 13

Refine

w + \frac{1}{w} = 13

Multiply both sides by

w

w^{2} + 1 = 13 w

Solve

w^{2} + 1 = 13 w : w = \frac{13 + 165}{2}, w = \frac{13 - 165}{2}

w = \frac{13 + 165}{2}, w = \frac{13 - 165}{2}

Verify Solutions

Find undefined (singularity) points:

w = 0

Combine undefined points with solutions:

w = \frac{13 + 165}{2}, w = \frac{13 - 165}{2}

\frac{1}{3 x - \frac{1}{3}} = 12

\frac{8}{3 x - 2} + \frac{6}{x + 1} = 2

x^{- 2} - 3 x^{- 1} + 2 = 0

0.08 = 1 - \frac{1127}{x}

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

What is the answer to w+w^{-1}=13 ?
The answer to w+w^{-1}=13 is w=(13+sqrt(165))/2 ,w=(13-sqrt(165))/2
Solve for w: w+w^{-1}=13
The solution is w=(13+sqrt(165))/2 ,w=(13-sqrt(165))/2