What are the solutions to the equation x^1+x^2+x^3=1 ?

The solutions to the equation x^1+x^2+x^3=1 are x\approx 0.54368…

Find the zeros of x^1+x^2+x^3=1

The zeros of x^1+x^2+x^3=1 are x\approx 0.54368…

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

x \approx 0.54368 \dots

Solution steps

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

Refine

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

Move

1

to the left side

x + x^{2} + x^{3} - 1 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{3} + x^{2} + x - 1 = 0

Find one solution for

x^{3} + x^{2} + x - 1 = 0

using Newton-Raphson:

x \approx 0.54368 \dots

Apply long division:

\frac{x ^{3} + x ^{2} + x - 1}{x - 0.54368 \dots} = x^{2} + 1.54368 \dots x + 1.83928 \dots

x^{2} + 1.54368 \dots x + 1.83928 \dots \approx 0

Find one solution for

x^{2} + 1.54368 \dots x + 1.83928 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.54368 \dots

y^{4} + 2 y^{2} + 1 = 0

x^{2} - x^{3} - 2 x^{2} + 2 x + 1 = 0

c^{4} x^{2} (c) = 12 x^{5}

x^{6} = - 1

x^{6} = 36

What are the solutions to the equation x^1+x^2+x^3=1 ?
The solutions to the equation x^1+x^2+x^3=1 are x\approx 0.54368…
Find the zeros of x^1+x^2+x^3=1
The zeros of x^1+x^2+x^3=1 are x\approx 0.54368…