Stage: 5 Challenge Level: 
Show that $x = 1$ is a solution of the equation
$x^{3/2} - 8x^{-3/2} = 7$
and explain why this is so. Find all the solutions of the equation.
Visualising. Generalising. Manipulating algebraic expressions/formulae. Number theory. Complex numbers. Mathematical reasoning & proof. Inequality/inequalities. Roots of complex numbers. Quadratic equations. Golden ratio.
Published June 2002.
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