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BALKAN-SL 2014 A4

    A4\boxed{A4} Let m1,m2,m3,n1,n2m_1,m_2,m_3,n_1,n_2 and n3n_3 be positive real numbers such that (m1−n1)(m2−n2)(m3−n3)=m1m2m3−n1n2n3(m_1-n_1)(m_2-n_2)(m_3-n_3)=m_1m_2m_3-n_1n_2n_3 Prove that (m1+n1)(m2+n2)(m3+n3)≥8m1m2m3(m_1+n_1)(m_2+n_2)(m_3+n_3)\geq8m_1m_2m_3

    Dataset text AI-MO AoPS. Quoted with source.

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