Question

0 = (1/2)x^3-x

How do I solve this? Please don't just answer it. I know it is 0 and sqrt(2), but I don't know how to solve this.

Answer 1

0 = (1/2)x^3-x


(1/2)x^3-x = 0


x^3-2x = 0


x(x^2 - 2) = 0


Can you take it from here?

Answer 2

What do you do with x^2-2? How do you get sqrt(2) from that?

Answer 3

0 = (1/2)x^3-x


(1/2)x^3-x = 0


x^3-2x = 0


x(x^2 - 2) = 0


x = 0 or x^2 - 2 = 0


x = 0 or x^2 = 2


x = 0 or x = sqrt(2) or x = -sqrt(2)

Answer 4

Nice. Why is it plus or minus sqrt(2)? Why not just plus?

Answer 5

because both sqrt(2) and -sqrt(2) square back to 2


(sqrt(2))^2 = 2

(-sqrt(2))^2 = 2

Answer 6

Thank you so much :)

Answer 7

you're welcome