MathDB

Math Prize 2013 Problem 16

Source:

September 10, 2013

Problem Statement

-3 \le x < \frac{3}{2}

and

x \ne 1

, define

C(x) = \frac{x^3}{1 - x}

. The real root of the cubic

2x^3 + 3x - 7

is of the form

p C^{-1}(q)

, where

p

and

q

are rational numbers. What is the ordered pair

(p, q)