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

The solutions to the equation (1-x)^3=x^2+x are x\approx 0.28477…

Find the zeros of (1-x)^3=x^2+x

The zeros of (1-x)^3=x^2+x are x\approx 0.28477…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(1 - x)^{3} = x^{2} + x

x \approx 0.28477 \dots

Solution steps

(1 - x)^{3} = x^{2} + x

Expand

(1 - x)^{3} : 1 - 3 x + 3 x^{2} - x^{3}

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

Move

x

to the left side

- x^{3} + 3 x^{2} - 4 x + 1 = x^{2}

Move

x^{2}

to the left side

- x^{3} + 2 x^{2} - 4 x + 1 = 0

Find one solution for

- x^{3} + 2 x^{2} - 4 x + 1 = 0

using Newton-Raphson:

x \approx 0.28477 \dots

Apply long division:

\frac{- x ^{3} + 2 x ^{2} - 4 x + 1}{x - 0.28477 \dots} = - x^{2} + 1.71522 \dots x - 3.51154 \dots

- x^{2} + 1.71522 \dots x - 3.51154 \dots \approx 0

Find one solution for

- x^{2} + 1.71522 \dots x - 3.51154 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.28477 \dots

x^{3} + x + 6 = 0

3 x^{3} + 9 x^{2} - 210 x = 0

(- x - 3)^{3} = 0

6 = \frac{4}{3} y^{34} y

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

What are the solutions to the equation (1-x)^3=x^2+x ?
The solutions to the equation (1-x)^3=x^2+x are x\approx 0.28477…
Find the zeros of (1-x)^3=x^2+x
The zeros of (1-x)^3=x^2+x are x\approx 0.28477…