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

The solutions to the equation x^2+x^3=1 are x\approx 0.75487…

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

The zeros of x^2+x^3=1 are x\approx 0.75487…

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

x \approx 0.75487 \dots

Solution steps

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

Move

1

to the left side

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} - 1 = 0

Find one solution for

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

using Newton-Raphson:

x \approx 0.75487 \dots

Apply long division:

\frac{x ^{3} + x ^{2} - 1}{x - 0.75487 \dots} = x^{2} + 1.75487 \dots x + 1.32471 \dots

x^{2} + 1.75487 \dots x + 1.32471 \dots \approx 0

Find one solution for

x^{2} + 1.75487 \dots x + 1.32471 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.75487 \dots

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

2 x^{3} + 3 x^{2} - 12 x - 10 = 0

A, A^{3} = A^{2} B - 3 A^{2}

w^{3} = - 2 - 2 i 3

(x^{2} - x)^{2} - (x^{2} - x) - 12 = 0

What are the solutions to the equation x^2+x^3=1 ?
The solutions to the equation x^2+x^3=1 are x\approx 0.75487…
Find the zeros of x^2+x^3=1
The zeros of x^2+x^3=1 are x\approx 0.75487…