What is the answer to x=(2+sqrt(3)x^4+1)/((x^4)) ?

The answer to x=(2+sqrt(3)x^4+1)/((x^4)) is x\approx 1.94267…

Solve for x: x=(2+sqrt(3)x^4+1)/((x^4))

The solution is x\approx 1.94267…

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x = \frac{2 + 3 x ^{4} + 1}{( x ^{4} )}

x \approx 1.94267 \dots

Solution steps

x = \frac{2 + 3 x ^{4} + 1}{( x ^{4} )}

Simplify

\frac{2 + 3 x ^{4} + 1}{x ^{4}} : \frac{3 x ^{4} + 3}{x ^{4}}

x = \frac{3 x ^{4} + 3}{x ^{4}}

Multiply both sides by

x^{4}

x^{5} = 3 x^{4} + 3

Solve

x^{5} = 3 x^{4} + 3 : x \approx 1.94267 \dots

x \approx 1.94267 \dots

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x \approx 1.94267 \dots

\frac{x \cdot ( x ^{6} - 1 )}{( x ^{8} + 1 )} = \frac{8}{17}

x - \frac{6}{3} x + 1 - x + \frac{6}{3} x - 1 = 3 x + \frac{2}{( x - 1 )} (x + 3)

50 = \frac{0.0023}{x}

\frac{3}{4 x ( x )} = 60

2 x^{- 2} = 1

What is the answer to x=(2+sqrt(3)x^4+1)/((x^4)) ?
The answer to x=(2+sqrt(3)x^4+1)/((x^4)) is x\approx 1.94267…
Solve for x: x=(2+sqrt(3)x^4+1)/((x^4))
The solution is x\approx 1.94267…