What are the solutions to the equation x^3=x^2+x-1 ?

The solutions to the equation x^3=x^2+x-1 are x=1,x=-1

Find the zeros of x^3=x^2+x-1

The zeros of x^3=x^2+x-1 are x=1,x=-1

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

x = 1, x = - 1

Solution steps

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

Move

1

to the left side

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

Move

x

to the left side

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

Move

x^{2}

to the left side

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x + 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 1 = 0 : x = - 1

The solutions are

x = 1, x = - 1

s^{5} + 5 s^{3} + 9 s^{2} + 7 s + 2 = 0

2 x^{3} + x - 18 = 0

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

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

- 4 x^{3} + 6 x^{2} + 8 = 0

What are the solutions to the equation x^3=x^2+x-1 ?
The solutions to the equation x^3=x^2+x-1 are x=1,x=-1
Find the zeros of x^3=x^2+x-1
The zeros of x^3=x^2+x-1 are x=1,x=-1