MathDB

6

Part of 2013 India National Olympiad

Problems(1)

a,b,c,x,y,z>0; a+b+c=x+y+z, abc=xyz

Source: INMO 2013 P6

2/3/2013
Let a,b,c,x,y,za,b,c,x,y,z be six positive real numbers satisfying x+y+z=a+b+cx+y+z=a+b+c and xyz=abc.xyz=abc. Further, suppose that a≤x<y<z≤ca\leq x<y<z\leq c and a<b<c.a<b<c. Prove that a=x,b=ya=x,b=y and c=z.c=z.
algebrapolynomialfunctioninequalitieslogarithmsinequalities proposed