1. Suppose that a, b, and c are real numbers such that a < b < c and a^3 − 3a + 1 = b^3 − 3b + 1 = c^3 − 3c + 1 = 0 .
Then (1/(a^2 + b)) + (1/(b^2 + c)) + (1/(c^2 + a)) can be written as (p/q) for relatively prime of positive integers p and q. Find 100p + q