Modules

[Victoria124]

How i solve this exercise: a,b,c =>0.Prove that |a-b|+|b-c|+|c-a|=2max{a,b,c} if and only if abc=0??
{}-is the fractional part of a number

 

[HallsofIvy]

If { } is "the fractional part of a number", what is meant by the fractional part of three numbers?

 

[Victoria124]

It is not the fractional part of the three numbers,it's the maximum fractional part of these three numbers .For example max{1,3;2,5;5,6}is 0,6.

 

[daon2]

How i solve this exercise: a,b,c =>0.Prove that |a-b|+|b-c|+|c-a|=2max{a,b,c} if and only if abc=0??
{}-is the fractional part of a number

This is not true. For a counter-example, let a=0, b=0.1, c=1.1.

Instead I think max{a,b,c} actually means the maximum of a,b,c. Then this statement is true.

For (=>) assume without loss of generality that a>=b >=c (justify why you can assume this). Then you get (a-b)+(b-c)+(a-c)=2a. So what does c equal? abc?

And for (<=), if abc=0, assume without loss of generality that a=0 and b>=c. From here it's straight forward.

 

[Victoria124]

Thank you very much, I managed to solve it .