The triangle inequalities make x=(a+b−c)/2x=(a+b-c)/2x=(a+b−c)/2, y=(a+c−b)/2y=(a+c-b)/2y=(a+c−b)/2, and z=(b+c−a)/2z=(b+c-a)/2z=(b+c−a)/2 positive. Thus write a=x+ya=x+ya=x+y, b=x+zb=x+zb=x+z, c=y+zc=y+zc=y+z.