olymmath

BALKAN-SL 2019 A5

    Let a,b,ca, b, c be positive real numbers, such that (ab)2+(bc)2+(ca)2=3(a b)^{2}+(b c)^{2}+(c a)^{2}=3. Prove that

    (a2−a+1)(b2−b+1)(c2−c+1)≥1.\left(a^{2}-a+1\right)\left(b^{2}-b+1\right)\left(c^{2}-c+1\right) \geq 1 .

    Dataset text NuminaMath olympiads. Quoted with source.

    Solutions

    No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

    Add a solution

    Locator balkan-sl/2019/a5 · Tag SV9ZAN8W60 · Edit this page on GitHub · Keys: j next, k previous