Amazing Math Olympiad problem| Can you get the three values of x?

A math OLYMPIAD algebra question. The three values of x were obtained. #matholympiadquestions #algebra

[@RyanLewis-Johnson-wq6xs]

X^3=4/27-X^2 X=-2/3=-0.6 recurring X=1/3=0.3 recurring

[@ichdu6710]

classical solution:
after inspecting the equation we found that x = 1/3 must be a solution.
Find the other solutions by using one of the following factorizing methods:
Method 1:
(x - 1/3)(x² + ax +4/9) = 0, find a by comparising left and right sides
Method 2:
use polynomial division to find the quadratric equation
Solve the quadratic equation with the abc formula.

[@JJONLINEMATHSCLASSchannel]

Thanks for contributing

[@عبدالواسع-س8م]

Thanks for your efforts.

[@harrymatabal8448]

Remainder and factor theorem ❤. Excellent explanation

[@JJONLINEMATHSCLASSchannel]

Thanks

[@garryfrancois2320]

JJ,
you are a talented math teacher.

[@JJONLINEMATHSCLASSchannel]

Thanks

[@harrymatabal8448]

Because we have 4/27 i would try
x = 1/3 and test yo see whether it is correct. If it is correct then 3x-1 is a factor. By division i hope to find the second factor. Factorize this trinomial. Etc. etc. etc😂

[@JJONLINEMATHSCLASSchannel]

👍👍

[@rezamohamadakhavan_abdolla8627]

Very difficult to follow