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

The solutions to the equation x-x^3=1 are x\approx-1.32471…

Find the zeros of x-x^3=1

The zeros of x-x^3=1 are x\approx-1.32471…

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x - x^{3} = 1

x \approx - 1.32471 \dots

Solution steps

x - x^{3} = 1

Move

1

to the left side

x - x^{3} - 1 = 0

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx - 1.32471 \dots

Apply long division:

\frac{- x ^{3} + x - 1}{x + 1.32471 \dots} = - x^{2} + 1.32471 \dots x - 0.75487 \dots

- x^{2} + 1.32471 \dots x - 0.75487 \dots \approx 0

Find one solution for

- x^{2} + 1.32471 \dots x - 0.75487 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.32471 \dots

x^{3} - 6 x + 4 = 0

x^{3} = - 0.49

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

x^{3} - 3 x^{2} - 18 x + 54 = 0

2 x^{3} - 8 x = 0

What are the solutions to the equation x-x^3=1 ?
The solutions to the equation x-x^3=1 are x\approx-1.32471…
Find the zeros of x-x^3=1
The zeros of x-x^3=1 are x\approx-1.32471…