MathDB

44

Part of 1984 IMO Longlists

Problems(1)

System of equations

Source: IMO Shortlist

11/1/2006
Let a,b,ca,b,c be positive numbers with a+b+c=32\sqrt{a}+\sqrt{b}+\sqrt{c}= \frac{\sqrt{3}}{2} Prove that the system of equations y−a+z−a=1\sqrt{y-a}+\sqrt{z-a}=1 z−b+x−b=1\sqrt{z-b}+\sqrt{x-b}=1 x−c+y−c=1\sqrt{x-c}+\sqrt{y-c}=1 has exactly one solution (x,y,z)(x,y,z) in real numbers. It was proposed by Poland. Have fun! :lol:
algebrasystem of equationsPythagorean TheoremgeometryIMO ShortlistIMO 1984