MathDB

2013 PUMaC Algebra A3

Source:

November 22, 2013

Problem Statement

Let

x_1=\sqrt{10}

and

y_1=\sqrt3

. For all

n\geq 2

, let \begin{align*}x_n&=x_{n-1}\sqrt{77}+15y_{n-1}\\y_n&=5x_{n-1}+y_{n-1}\sqrt{77}\end{align*} Find

x_5^6+2x_5^4-9x_5^4y_5^2-12x_5^2y_5^2+27x_5^2y_5^4+18y_5^4-27y_5^6.