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

The solutions to the equation 1-3x+x^2-x^3=x are x\approx 0.26272…

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

The zeros of 1-3x+x^2-x^3=x are x\approx 0.26272…

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

x \approx 0.26272 \dots

Solution steps

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

Move

x

to the left side

- x^{3} + x^{2} - 4 x + 1 = 0

Find one solution for

- x^{3} + x^{2} - 4 x + 1 = 0

using Newton-Raphson:

x \approx 0.26272 \dots

Apply long division:

\frac{- x ^{3} + x ^{2} - 4 x + 1}{x - 0.26272 \dots} = - x^{2} + 0.73727 \dots x - 3.80630 \dots

- x^{2} + 0.73727 \dots x - 3.80630 \dots \approx 0

Find one solution for

- x^{2} + 0.73727 \dots x - 3.80630 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.26272 \dots

5 x^{3} - 3 x^{2} + 180 x - 108

y, x^{3} = 4 y^{2} + 4 y - 3

x^{4} - 128 \cdot x^{2} - 8192 \cdot x - 61440 = 0

6 x^{3} - 5 x - 1 = 0

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

What are the solutions to the equation 1-3x+x^2-x^3=x ?
The solutions to the equation 1-3x+x^2-x^3=x are x\approx 0.26272…
Find the zeros of 1-3x+x^2-x^3=x
The zeros of 1-3x+x^2-x^3=x are x\approx 0.26272…