algèbre lycée inégalitésmoyennes
A symmetric inequality
Sélection COMIMa · 2026 · Madagascar · ★★★★★
Statement
Soient $a$, $b$ et $c$ des réels strictement positifs tels que $abc = 1$.
Montrer que \[ a^2 + b^2 + c^2 \geqslant a + b + c. \]
Préciser les cas d'égalité.
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Source & credits
Origin : Sélection COMIMa · 2026 · Madagascar
Reproduced for non-commercial educational purposes. Rights to the original statement belong to its authors / the competition organiser.
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