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,