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Enshrouded_

Member

Registered: 2015-07-31

Posts: 47

Absolute Value Problems

Suppose that

What is the maximum possible value of

?

Suppose that

What is the maximum possible value of

?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,166

Re: Absolute Value Problems

Q1.  Suppose P, Q and R are points on a number line with P > Q > R.

Then |P-Q| is the distance PQ; |Q-R| is the distance QR; and |R-P| is the distance PR, and PR = PQ + QR.

And if PQ + QR + RQ = 20, then PR = 10 and both PQ and QR < 10

So if we replace P, Q and R with a, b and c in some (at present unknown) order the biggest we can get  for |a-b| is 10.

Still wondering if I'll ever be able to do Q2. 

Is that meant to be |a-n| or should it be |a-b| ?

Oh hang on.  Maybe:

Consider A, B, ... Z are points on a number line with A > B > ... > Z.

Note I'm not assuming that A = a and so on, but I'm left with no new letters for this.

|A-B| + |B-C| + ..... + |Y-Z| = |Z-A| 

So could this answer also be 10 ?

Bob

Last edited by Bob (2015-08-19 23:41:39)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Enshrouded_

Member

Registered: 2015-07-31

Posts: 47

Re: Absolute Value Problems

Thanks! I thought 10 would be the first answer but didnt know how to prove it
For the second I guess we use the same reasoning for the first.