Specimen Cyprus Seniors Provincial/2nd grade/Problem 4
Problem
If are the roots of equation then:
a) Prove that and
b) Calculate the value of: .
Solution
Since , we can multiply both sides by , and will still satisfy the equation:
Thus, as desired .
The third roots of are , , and .
Since , we have and . (Switching the two values will not affect the result).
Note that , and that
So,