SMO Junior · 4. Inequalities, extreme values and the integer part
Use the rules of inequalities safely, find extreme values by completing squares, by distances and reflections, and by AM–GM, and compute integer parts by squeezing numbers between consecutive integers.
Apply the rules of inequalities, paying attention to signs, and recognise false statements by counterexamples.
Find minima and maxima by completing squares, always with an attained equality case.
Interpret absolute values and square roots as distances and use the triangle inequality and reflections.
Compute integer parts by squeezing, using conjugates and bounds on terms.
Prove inequalities with AM–GM by splitting terms and matching equality cases.