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}

Making and proving conjectures. Golden ratio. Quadratic equations. Mathematical reasoning & proof. Inequalities. Simultaneous equations. Powers & roots. Surds. Creating and manipulating expressions and formulae. Fibonacci sequence.

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Surds

Age 14 to 16 Challenge Level: