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BALKAN-SL 2019 A3

    Let a,b,ca, b, c be real numbers such that 0≤a≤b≤c0 \leq a \leq b \leq c. Prove that if

    a+b+c=ab+bc+ca>0,a+b+c=a b+b c+c a>0,

    then bc(a+1)≥2\sqrt{b c}(a+1) \geq 2. When does the equality hold?

    Dataset text NuminaMath olympiads. Quoted with source.

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