What is the answer to x^{-2}-3x^{-1}+1/5 =0 ?

The answer to x^{-2}-3x^{-1}+1/5 =0 is x=(15+sqrt(205))/2 ,x=(15-sqrt(205))/2

Solve for x: x^{-2}-3x^{-1}+1/5 =0

The solution is x=(15+sqrt(205))/2 ,x=(15-sqrt(205))/2

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x^{- 2} - 3 x^{- 1} + \frac{1}{5} = 0

x = \frac{15 + 205}{2}, x = \frac{15 - 205}{2}

Decimal Notation

x = 14.65891 \dots, x = 0.34108 \dots

Solution steps

x^{- 2} - 3 x^{- 1} + \frac{1}{5} = 0

Refine

\frac{1}{x ^{2}} - \frac{3}{x} + \frac{1}{5} = 0

Multiply by LCM

5 - 15 x + x^{2} = 0

Solve

5 - 15 x + x^{2} = 0 : x = \frac{15 + 205}{2}, x = \frac{15 - 205}{2}

x = \frac{15 + 205}{2}, x = \frac{15 - 205}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{15 + 205}{2}, x = \frac{15 - 205}{2}

u - 12 (u)^{- 1} - 1 = 0

- \frac{8}{( x - 2 ) ^{2}} = - 2

\frac{a}{a - 1} = - \frac{4}{3}

\frac{4 x - 6}{x - 7} = \frac{1}{2}

2 = - 6 + \frac{8}{x ^{2}}

What is the answer to x^{-2}-3x^{-1}+1/5 =0 ?
The answer to x^{-2}-3x^{-1}+1/5 =0 is x=(15+sqrt(205))/2 ,x=(15-sqrt(205))/2
Solve for x: x^{-2}-3x^{-1}+1/5 =0
The solution is x=(15+sqrt(205))/2 ,x=(15-sqrt(205))/2