What is the answer to solvefor x,11-1/x =x ?

The answer to solvefor x,11-1/x =x is x=(11+3sqrt(13))/2 ,x=(11-3sqrt(13))/2

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solvefor x,11-1/x =x

solve for

x, 11 - \frac{1}{x} = x

x = \frac{11 + 3 13}{2}, x = \frac{11 - 3 13}{2}

Decimal Notation

x = 10.90832 \dots, x = 0.09167 \dots

Solution steps

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

Multiply both sides by

x

11 x - 1 = x^{2}

Solve

11 x - 1 = x^{2} : x = \frac{11 + 3 13}{2}, x = \frac{11 - 3 13}{2}

x = \frac{11 + 3 13}{2}, x = \frac{11 - 3 13}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{11 + 3 13}{2}, x = \frac{11 - 3 13}{2}

(y^{- 2}) = \frac{1}{y ^{2}}

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

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

\frac{1}{x ^{2} + y ^{2}} = 0

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

What is the answer to solvefor x,11-1/x =x ?
The answer to solvefor x,11-1/x =x is x=(11+3sqrt(13))/2 ,x=(11-3sqrt(13))/2