Stage: 5 Challenge Level: 
Find the range of values of $x$ for which \[ {\sqrt{x}+ {{1}\over{\sqrt{x}}}} {4} \] where $\sqrt{x}$ is the positive root.
Long problems. Manipulating algebraic expressions/formulae. Complex numbers. Surds. Quadratic equations. Inequality/inequalities. Mathematical reasoning & proof. Fibonacci sequence. Powers & roots. Golden ratio.
Published December 2001,January 2002,March 2009,April 2009.
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email: nrich@damtp.cam.ac.uk
