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

The solutions to the equation x(x^2-2)=2 are x\approx 1.76929…

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

The zeros of x(x^2-2)=2 are x\approx 1.76929…

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

x \approx 1.76929 \dots

Solution steps

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

Expand

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

x^{3} - 2 x = 2

Move

2

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx 1.76929 \dots

Apply long division:

\frac{x ^{3} - 2 x - 2}{x - 1.76929 \dots} = x^{2} + 1.76929 \dots x + 1.13039 \dots

x^{2} + 1.76929 \dots x + 1.13039 \dots \approx 0

Find one solution for

x^{2} + 1.76929 \dots x + 1.13039 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.76929 \dots

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

6 \cdot x^{3} = 180

x^{6} + x^{4} + x - 2 = 0

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

20 x^{3} - 12 x^{2} - 20 x = 0

What are the solutions to the equation x(x^2-2)=2 ?
The solutions to the equation x(x^2-2)=2 are x\approx 1.76929…
Find the zeros of x(x^2-2)=2
The zeros of x(x^2-2)=2 are x\approx 1.76929…