What are the solutions to the equation 0=1-x-x^3 ?

The solutions to the equation 0=1-x-x^3 are x\approx 0.68232…

Find the zeros of 0=1-x-x^3

The zeros of 0=1-x-x^3 are x\approx 0.68232…

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0 = 1 - x - x^{3}

x \approx 0.68232 \dots

Solution steps

0 = 1 - x - x^{3}

Switch sides

1 - x - x^{3} = 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 0.68232 \dots

Apply long division:

\frac{- x ^{3} - x + 1}{x - 0.68232 \dots} = - x^{2} - 0.68232 \dots x - 1.46557 \dots

- x^{2} - 0.68232 \dots x - 1.46557 \dots \approx 0

Find one solution for

- x^{2} - 0.68232 \dots x - 1.46557 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.68232 \dots

m^{3} + 3 m^{2} + 3 m + 1 = 0

x^{3} - 3 x^{2} + 2 x - 7 = 0

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

3 t^{4} - t^{2} - 2 = 0

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

What are the solutions to the equation 0=1-x-x^3 ?
The solutions to the equation 0=1-x-x^3 are x\approx 0.68232…
Find the zeros of 0=1-x-x^3
The zeros of 0=1-x-x^3 are x\approx 0.68232…