The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

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}