Browse · MathNet Print → 55rd Ukrainian National Mathematical Olympiad - Third Round Ukraine algebra Problem Prove the inequality for positive a, b, c, d cd(a+b)2+ab(c+d)2≥8. Solution — click to reveal Use two inequalities of means: cd(a+b)2+ab(c+d)2≥cd4ab+ab4cd≥2⋅4cdab⋅abcd=8. Techniques QM-AM-GM-HM / Power Mean ← Previous problem Next problem →