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

The solutions to the equation 2x^3=(x-1)^3 are x\approx-3.84732…

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

The zeros of 2x^3=(x-1)^3 are x\approx-3.84732…

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

x \approx - 3.84732 \dots

Solution steps

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

Expand

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

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

Switch sides

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

Move

2 x^{3}

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx - 3.84732 \dots

Apply long division:

\frac{- x ^{3} - 3 x ^{2} + 3 x - 1}{x + 3.84732 \dots} = - x^{2} + 0.84732 \dots x - 0.25992 \dots

- x^{2} + 0.84732 \dots x - 0.25992 \dots \approx 0

Find one solution for

- x^{2} + 0.84732 \dots x - 0.25992 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 3.84732 \dots

16 x = 2 x^{4}

- 3 x (2 x - 5) (x^{2} + 25) = 0

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

x^{6} - 7 x^{3} = 8

t^{4} = 3

What are the solutions to the equation 2x^3=(x-1)^3 ?
The solutions to the equation 2x^3=(x-1)^3 are x\approx-3.84732…
Find the zeros of 2x^3=(x-1)^3
The zeros of 2x^3=(x-1)^3 are x\approx-3.84732…