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

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

Find the zeros of 3x=x^3

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

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3 x = x^{3}

x = 0, x = - 3, x = 3

Decimal Notation

x = 0, x = - 1.73205 \dots, x = 1.73205 \dots

Solution steps

3 x = x^{3}

Switch sides

x^{3} = 3 x

Move

3 x

to the left side

x^{3} - 3 x = 0

Factor

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

x (x + 3) (x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 3 = 0 or x - 3 = 0

Solve

x + 3 = 0 : x = - 3

Solve

x - 3 = 0 : x = 3

The solutions are

x = 0, x = - 3, x = 3

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

50 x - 25 = 2 x^{3} - x^{2}

x^{3} + 729 = 0

2 x^{3} + 3 x^{2} - 10 x - 15 = 0

z^{5} + 32 i = 0

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