MathDB
System has exactly one real solution

Source:

September 8, 2010
algebrasystem of equationsIMO ShortlistPythagorean Theoremgeometry

Problem Statement

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.
Back to ProblemsView on AoPS