OpenStudy (anonymous):

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.

6 years ago
jimthompson5910 (jim_thompson5910):

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?

6 years ago
OpenStudy (anonymous):

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

6 years ago
jimthompson5910 (jim_thompson5910):

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)

6 years ago
OpenStudy (anonymous):

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

6 years ago
jimthompson5910 (jim_thompson5910):

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

6 years ago
OpenStudy (anonymous):

Thank you so much :)

6 years ago
jimthompson5910 (jim_thompson5910):

you're welcome

6 years ago