Stage: 4 Challenge Level: 
Find the exact values of $x$, $y$ and $a$ satisfying the following system of equations: $$\frac{1}{a+1}=a-1$$ $$x+y=2a$$ $$x=ay$$
Golden ratio. Quadratic equations. Stage 5 - Core Mapping. Simultaneous equations. Manipulating algebraic expressions/formulae. Powers & roots. Stage 5 - Reviewed 2012. Working systematically. Fibonacci sequence. Surds.
Published January 1999.
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