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

The answer to x+x^{-1}=2 is x=1

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x+x^{-1}=2

x + x^{- 1} = 2

x = 1

Solution steps

x + x^{- 1} = 2

Refine

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

Multiply both sides by

x

x^{2} + 1 = 2 x

Solve

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

x = 1

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 1

\frac{x ^{3} + 12 x}{6 x ^{2} + 8} = \frac{35}{19}

x, \frac{4}{x} - \frac{5}{y} = x + \frac{y}{x} y + \frac{3}{10}

\frac{4}{( x + 1 )} + \frac{5}{x} - \frac{9}{( 3 x - 1 )} = 0

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

\frac{( 5 + 6 ) ( n - 4 )}{( 7 - 3 n ) + 7 n ( 4 - 1 n )} = 6