What are the solutions to the equation 4=x^3-3x ?

The solutions to the equation 4=x^3-3x are x\approx 2.19582…

Find the zeros of 4=x^3-3x

The zeros of 4=x^3-3x are x\approx 2.19582…

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4 = x^{3} - 3 x

x \approx 2.19582 \dots

Solution steps

4 = x^{3} - 3 x

Switch sides

x^{3} - 3 x = 4

Move

4

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx 2.19582 \dots

Apply long division:

\frac{x ^{3} - 3 x - 4}{x - 2.19582 \dots} = x^{2} + 2.19582 \dots x + 1.82164 \dots

x^{2} + 2.19582 \dots x + 1.82164 \dots \approx 0

Find one solution for

x^{2} + 2.19582 \dots x + 1.82164 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 2.19582 \dots

4 x^{3} + 12 x = 0

2 x^{3} + 9 x^{2} + 2 x - 30 = 0

x^{4} - x^{3} - 5 x^{2} - 12 x + 56 = 0

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

x^{3} - 8 x^{2} + 17 x - 30 = 0

What are the solutions to the equation 4=x^3-3x ?
The solutions to the equation 4=x^3-3x are x\approx 2.19582…
Find the zeros of 4=x^3-3x
The zeros of 4=x^3-3x are x\approx 2.19582…