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

The solutions to the equation x^3-x^2=x are x=0,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

Find the zeros of x^3-x^2=x

The zeros of x^3-x^2=x are x=0,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

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

x = 0, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

Decimal Notation

x = 0, x = 1.61803 \dots, x = - 0.61803 \dots

Solution steps

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

Move

x

to the left side

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

Factor

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

x (x^{2} - x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - x - 1 = 0

Solve

x^{2} - x - 1 = 0 : x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

The solutions are

x = 0, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

x^{4} + 6 x^{2} - 7 = 0

10 = - c^{3} + 9

\frac{( 4 x - 7 ) ^{3}}{3} = 27

x^{4} = - 9

2 x^{3} + x^{2} - x + 6 = 0

What are the solutions to the equation x^3-x^2=x ?
The solutions to the equation x^3-x^2=x are x=0,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2
Find the zeros of x^3-x^2=x
The zeros of x^3-x^2=x are x=0,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2