What is the answer to u+u^{-1}= 5/2 ?

The answer to u+u^{-1}= 5/2 is u=2,u= 1/2

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u+u^{-1}= 5/2

u + u^{- 1} = \frac{5}{2}

u = 2, u = \frac{1}{2}

Decimal Notation

u = 2, u = 0.5

Solution steps

u + u^{- 1} = \frac{5}{2}

Refine

u + \frac{1}{u} = \frac{5}{2}

Multiply by LCM

2 u^{2} + 2 = 5 u

Solve

2 u^{2} + 2 = 5 u : u = 2, u = \frac{1}{2}

u = 2, u = \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

u = 0

Combine undefined points with solutions:

u = 2, u = \frac{1}{2}

\frac{2}{x - 4} + \frac{x + 1}{3} = 5

a^{2} = \frac{- k ^{2}}{1 - k}

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

2 x + 1 = \frac{15}{x}

\frac{11}{x + 1} = \frac{3}{x - 1}