MathDB

9.1

Part of 2006 Moldova National Olympiad

Problems(1)

Moldova MO 2006, 9.1 (tricky ineq.)

Source: Moldova national olympiad 2006, grade 9, pr.1

9/21/2016
Let a,b,ca,b,c be positive real numbers such that a+b+c=2005a+b+c=2005. Find the minimum value of the expression: E=a2006+b2006+c2006+(ab)2004+(bc)2004+(ca)2004(abc)2004E=a^{2006}+b^{2006}+c^{2006}+\frac{(ab)^{2004}+(bc)^{2004}+(ca)^{2004}}{(abc)^{2004}}
inequalities