How would i solve x^3-2x+1=0?

Question

i kinda forgot basic algebra

Answer 1

x³ - 2x = - 1

x³ - x = - 1 + 1

x³ - x = 0

x³ = x

x³/x = x/x

x² = 1

x = 1

Answer: x = 1

Proof:

1³ - 2(1) = - 1

1 - 2 = - 1

- 1 = - 1

Answer 2

The easiest way to solve a cubic is with a graphing calculator.  Do you have one ?  

You can type the equation into y =

Then find the zeros ( which are x-intercepts)

x = 1 works

Good luck to you !

Answer 3

Ok, first note that x=1 solves the equation. This implies that you can factor out x-1:

x^3 - 2x + 1 = (x - 1)(x^2 + x -1)

Hence both roots of x^2 + x - 1 are solutions to your equation. To get those roots, note that

x^2 + x -1 = (x + 1/2)^2 - 5/4

and thus the other two solutions are

x = - 1/2 - sqrt(5)/2 and x = - 1/2 + sqrt(5)/2

Summary: the *three* solutions to your equation are

x = 1

x = - 1/2 - sqrt(5)/2

x = - 1/2 + sqrt(5)/2