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

The solutions to the equation (x^3)/3-x= x/3 are x=0,x=2,x=-2

Find the zeros of (x^3)/3-x= x/3

The zeros of (x^3)/3-x= x/3 are x=0,x=2,x=-2

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\frac{x ^{3}}{3} - x = \frac{x}{3}

x = 0, x = 2, x = - 2

Solution steps

\frac{x ^{3}}{3} - x = \frac{x}{3}

Multiply both sides by

3

x^{3} - 3 x = x

Move

x

to the left side

x^{3} - 4 x = 0

Find one solution for

x^{3} - 4 x = 0

using Newton-Raphson:

x \approx 0.00000 \dots

Apply long division:

\frac{x ^{3} - 4 x}{x} = x^{2} - 4

x^{2} - 4 \approx 0

Find one solution for

x^{2} - 4 = 0

using Newton-Raphson:

x \approx 2.00000 \dots

Apply long division:

\frac{x ^{2} - 4}{x - 2} = x + 2

x + 2 \approx 0

x \approx - 2

Approximate to algebraic form

x = - 2

Approximate to algebraic form

x \approx 0.00000 \dots : x = 0

x \approx 2.00000 \dots : x = 2

x = 0, x = 2, x = - 2

The solutions are

x = 0, x = 2, x = - 2

x^{4} - x^{3} - 11 x^{2} = x + 12

- 3 (9 x^{2} - 4) (x^{2} - 15) = 0

u^{5} = 243

x^{3} + 5 x^{2} - 11 x - 55 = 0

x^{3} + 21 x^{2} + 2520 x + 2500 = 0

What are the solutions to the equation (x^3)/3-x= x/3 ?
The solutions to the equation (x^3)/3-x= x/3 are x=0,x=2,x=-2
Find the zeros of (x^3)/3-x= x/3
The zeros of (x^3)/3-x= x/3 are x=0,x=2,x=-2