The Root of the Problem

Find the sum of this series of surds.

Fit for Photocopying

Explore the relationships between different paper sizes.

Surds

Age 14 to 16 Challenge Level:

Find the exact values of $x$, $y$ and $a$ satisfying the following system of equations:
\begin{align}
\frac{1}{a+1}&=a-1 \\
x+y&=2a \\
x&=ay
\end{align}