ax^5 + by^5
Source: USA AIME 1990, Problem 15
March 21, 2006
AMCAIMEVietaalgebrapolynomial
Problem Statement
Find if the real numbers , , , and satisfy the equations
\begin{eqnarray*} ax + by &=& 3, \\ ax^2 + by^2 &=& 7, \\ ax^3 + by^3 &=& 16, \\ ax^4 + by^4 &=& 42. \end{eqnarray*}