What is the answer to x^2+x^{-2}-6=0 ?

The answer to x^2+x^{-2}-6=0 is x=sqrt(2)+1,x=sqrt(2)-1

Solve for x: x^2+x^{-2}-6=0

The solution is x=sqrt(2)+1,x=sqrt(2)-1

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x^{2} + x^{- 2} - 6 = 0

x = 2 + 1, x = 2 - 1

Decimal Notation

x = 2.41421 \dots, x = 0.41421 \dots

Solution steps

x^{2} + x^{- 2} - 6 = 0

Refine

x^{2} + \frac{1}{x ^{2}} - 6 = 0

Multiply both sides by

x^{2}

x^{4} + 1 - 6 x^{2} = 0

Solve

x^{4} + 1 - 6 x^{2} = 0 : x = 2 + 1, x = 2 - 1

x = 2 + 1, x = 2 - 1

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 2 + 1, x = 2 - 1

0.27 = \frac{3}{x}

\frac{- 3}{- 9 x - 7} - 9 = 6

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

x = \frac{6 x + 7}{x - 1}

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

What is the answer to x^2+x^{-2}-6=0 ?
The answer to x^2+x^{-2}-6=0 is x=sqrt(2)+1,x=sqrt(2)-1
Solve for x: x^2+x^{-2}-6=0
The solution is x=sqrt(2)+1,x=sqrt(2)-1