15

Part of 1990 AIME Problems

Problems(1)

Source: USA AIME 1990, Problem 15

ax^5 + by^5

if the real numbers

a

b

x

y

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*}

AMCAIMEVietaalgebrapolynomial