Algebra help please :)?

Question

could someone please explain how to solve the equation

x^3-2x+1=0

thanks so much!

xoxo nikki

Answer 1

first you factor out and x out of the first two terms.

so u have   x(x^2-2)+1=0

then u think that u need x(x^2-2) to equal -1 because then u will add 1 and be left with 0 (-1+1=0)

so    x(x^2-2)=-1

now guess and check for x.

let's try x=1.

1(1^2-2)=?

1(1-2)=?

1(-1)=-1

close, but we need x to equal 1 not -1. so let's try x=-1

-1(-1^2-2)=?

-1(1-2)=?

-1(1)=-1

yey we got it. x=-1

Answer 2

first move the one to the other end

x^3 -2x = -1

take X as common factor

x(x^2-2) = - 1

it is either x = 1 or x = -1

Note here that X^2 will always be positive and (x^2-2) will always give  a negative answer.

so x must be = 1

check for it..

1^3 - 2*1 + 1 = 1 - 2 + 1 = 0

if we used -1

-1^3 -2*-1 + 1 = -1 + 2 + 1 = 2 which is wrong answer.