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

The solutions to the equation x^2+x+1=x^3+x^2+1 are x=0,x=-1,x=1

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

The zeros of x^2+x+1=x^3+x^2+1 are x=0,x=-1,x=1

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

x = 0, x = - 1, x = 1

Solution steps

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

Switch sides

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

Move

1

to the right side

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

Move

x

to the left side

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

Move

x^{2}

to the left side

x^{3} - x = 0

Factor

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

x (x + 1) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 1 = 0 or x - 1 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

x = 0, x = - 1, x = 1

x^{4} + 4 x^{2} - 5 = 0

6 x = (- 2 x)^{3}

10 x - 8 x^{2} - 2 x^{3} = 0

3 x^{4} - 48 = 0

x^{3} - 7 x^{2} + 3 x + 35 = 0

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