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# What a ... ! |2|S|S|=|S| Find all integer roots and post

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SVP
Joined: 03 Feb 2003
Posts: 1607
Followers: 7

Kudos [?]: 87 [0], given: 0

What a ... ! |2|S|S|=|S| Find all integer roots and post [#permalink]  06 Jun 2003, 01:35
What a ... !

|2|S|–S|=|S|

Find all integer roots and post your approach. It is interesting to take a look.
Intern
Joined: 05 Apr 2003
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 0

I think that the solution depends on the way we understand the equation. I found 2 cases with the following solutions:

1. S>=0

2. S= 0 or S=-1/2

Is that right?
_________________

Anh

Manager
Joined: 25 May 2003
Posts: 54
Followers: 1

Kudos [?]: 3 [0], given: 0

all positive integers and 0 work
CTO
Joined: 19 Dec 2002
Posts: 250
Location: Ukraine
Followers: 19

Kudos [?]: 36 [0], given: 9

S >= 0 [#permalink]  07 Jun 2003, 13:28
S >= 0.

S = - 1/2 - doesn't work, try it out again!

There're two sets of solutions:

1. S >= 0
|S| = S
|2|S| - S| = |2S-S| = |S| = S
Equality is reduced to S=S, i.e. all S >= 0 match;

2. S < 0
|S| = -S
|2|S| - S| = |-3S| = 3|S| = -3S
-3S = S
S = 0, which doesn't match S < 0. No solutions here.
SVP
Joined: 03 Feb 2003
Posts: 1607
Followers: 7

Kudos [?]: 87 [0], given: 0

skoper wrote:
all positive integers and 0 work

Skoper is right. -1/2 is not the answer. The answer is a row of nonnegative integers: 0, 1, 2, 3, and so on.

My approach is to square both parts, to take a common multiple, and then to check each root.
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