Stage: 5 Challenge Level: 
Given that $u> 0$ and $v> 0$ what is the smallest possible value of $1/u + 1/v$ given that $u + v = 5$?
Can you find this value by more than one method (not involving trial and error) without using calculus?
Graphs. Stage 5 - Reviewed 2012. Inequality/inequalities. Patterned numbers. Mathematical reasoning & proof. AM/GM inequality. Manipulating algebraic expressions/formulae. Number theory. Dynamical systems. Maximise/minimise/optimise.
Published March 2001.
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