Two Owls qualified for the American Invitational Math Exam (AIME). Freshman Dannie Dong and seventh-grader James Jin compete this month to qualify for the even-more selective group competing in the United States of America Junior Mathematical Olympiad in April.
A sample AIME question follows; send your answers to Dr. Steve Gadbois at your leisure:
Let p<q<r be the roots (solutions) of the equation 2014^(1/2) x^3 - 4029 x^2 + 2 = 0. Find the value of q(p+r).
First, note that 4029=1+2*2014.
Second, don't immediately try to find the individual values of p, q, or r.