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

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

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

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

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

x \approx - 0.75487 \dots

Solution steps

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

Move

1

to the left side

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

Move

x^{2}

to the left side

x^{3} + 1 - x^{2} = 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^{3} - 36 = 0

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

x^{4} + 6 x^{2} + 8

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

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

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