[tex]|a-b|=2|b-c|=3|c-a|\\\\|a-b|=2|b-c|\\a-b=2(b-c) \to a-b=2b-2c \to a+2c=3b\\-(a-b)=2(-(b-c)) \to -a+b=2(-b+c) \to b-a=-2b+2c \to 3b=2c+a\\\\2|b-c|=3|c-a|\\2(b-c)=3(c-a) \to 2b-2c=3c-3a \to 2b+3a=5c\\2(-(b-c))=3(-(c-a)) \to 2(-b+c)=3(-c+a) = -2b+2c=-3c+3a \to -2b-3a=-3c-2c \to -(2b+3a)=-5c \to 2b+3a=5c\\\\3b-2c=a\\2b+3(3b-2c)=5c\\2b+9b-6c=5c\\11b=5c+6c\\11b=11c /:11\\b=c\\\\a=3b-2c \to a=3c-2c \to a=c\\\\\underline{\bold{a=b=c}}[/tex]
