[tex]|a-b|=2|b-c|=3|c-a|[/tex]
[tex]I. \\|a-b|=2|b-c|\\a-b=2(b-c)\\a-b=2b-2c\\a+2c=2b+b\\a+2c=3b\\\\-(a-b)=-2(b-c)\\-a+b=-2b+2c\\-a-2c=-2b-b \\-(a+2c)=-3b /*(-1)\\a+2c=3b[/tex]
[tex]II. \\2|b-c|=3|c-a|\\2(b-c)=3(c-a)\\2b-2c=3c-3a\\2b+3a=3c+2c\\2b+3a=5c\\\\-2(b-c)=-3(c-a)\\-2b+2c=-3c+3a\\-2b-3a=-3c-2c\\-2b-3a=-5c\\-(2b+3a)=-5c /*(-1)\\2b+3a=5c[/tex]
[tex]III. \\a+2c=3b \to a=3b-2c\\\\2b+3a=5c\\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{a=b=c}[/tex]
