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

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

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

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

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

x = - 1, x = 1 + 2, x = 1 - 2

Decimal Notation

x = - 1, x = 2.41421 \dots, x = - 0.41421 \dots

Solution steps

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

Move

2

to the left side

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

Move

x^{2}

to the left side

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

Write in the standard form

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

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

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

The solutions are

x = - 1, x = 1 + 2, x = 1 - 2

9 x^{4} - 39 x^{3} + 55 x^{2} - 7 x - 10 = 0

10000000 = 2560000000 (x^{8})

3 x^{3} + 9 x - 1 = 0

15 x^{3} + 14 x^{2} - 8 x = 900

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

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