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An algebraic inequality for 4 variables

Source: The 31st Korean Mathematical Olympiad (for middle school students, 12 Nov. 2017)

November 13, 2017
inequalitiesKJMO

Problem Statement

4. Let a≥b≥c≥d>0a \geq b \geq c \geq d>0. Show that b3a+c3b+d3c+a3d+3(ab+bc+cd+da)≥4(a2+b2+c2+d2). \frac{b^3}{a} + \frac{c^3}{b} + \frac{d^3}{c} + \frac{a^3}{d} + 3 \left( ab+bc+cd+da \right) \geq 4 {\left( a^2 + b^2 + c^2 +d^2 \right)}. Other problems (in Korean) are also available at https://www.facebook.com/KoreanMathOlympiad
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