What is the answer to x^2+x+x^{-1}+x^{-2}=4 ?

The answer to x^2+x+x^{-1}+x^{-2}=4 is x=1,x=(-3+sqrt(5))/2 ,x=(-3-sqrt(5))/2

Solve for x: x^2+x+x^{-1}+x^{-2}=4

The solution is x=1,x=(-3+sqrt(5))/2 ,x=(-3-sqrt(5))/2

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

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

Decimal Notation

x = 1, x = - 0.38196 \dots, x = - 2.61803 \dots

Solution steps

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

Refine

x^{2} + x + \frac{1}{x} + \frac{1}{x ^{2}} = 4

Multiply by LCM

x^{4} + x^{3} + x + 1 = 4 x^{2}

Solve

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

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

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

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

m = \frac{( x ^{2} - 3 )}{( x ^{2} - 3 x + 3 )}

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

26 = \frac{n}{2 \cdot { 2 \cdot 6 + ( n - 1 ) \cdot 0.5 }}

(\frac{1}{8 - x})^{2} + 42 = \frac{( x + \frac{1}{8} ) ^{2} - x}{2 + x ( x - 1 )}

\frac{a + 4}{a} = \frac{4 a}{a ^{2} + a - 2}

What is the answer to x^2+x+x^{-1}+x^{-2}=4 ?
The answer to x^2+x+x^{-1}+x^{-2}=4 is x=1,x=(-3+sqrt(5))/2 ,x=(-3-sqrt(5))/2
Solve for x: x^2+x+x^{-1}+x^{-2}=4
The solution is x=1,x=(-3+sqrt(5))/2 ,x=(-3-sqrt(5))/2