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

The solutions to the equation x(x-1)^2=1 are x\approx 1.75487…

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

The zeros of x(x-1)^2=1 are x\approx 1.75487…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

x \approx 1.75487 \dots

Solution steps

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

Expand

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

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

Move

1

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx 1.75487 \dots

Apply long division:

\frac{x ^{3} - 2 x ^{2} + x - 1}{x - 1.75487 \dots} = x^{2} - 0.24512 \dots x + 0.56984 \dots

x^{2} - 0.24512 \dots x + 0.56984 \dots \approx 0

Find one solution for

x^{2} - 0.24512 \dots x + 0.56984 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.75487 \dots

x^{8} + 8 x^{4} + 16 = 0

x^{2015} = x^{2016}

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

2 x^{4} - 3 x^{3} + 12 x^{2} - 16 x + 5 = 0

2 x^{3} = 48

What are the solutions to the equation x(x-1)^2=1 ?
The solutions to the equation x(x-1)^2=1 are x\approx 1.75487…
Find the zeros of x(x-1)^2=1
The zeros of x(x-1)^2=1 are x\approx 1.75487…