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

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

Find the zeros of x^3-x=1

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

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x^{3} - x = 1

x \approx 1.32471 \dots

Solution steps

x^{3} - x = 1

Move

1

to the left side

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^{4} + 5 x^{2} + 4 = 0

(x + 4)^{3} = - 729

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

z^{6} + z^{3} + 1 = 0

x^{4} = \frac{16}{81}

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