## Problem Of The Week 36

**Find the value of the expression ……….|||||||x-2|+2|-2|+2|……….**

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**Find the value of the expression ……….|||||||x-2|+2|-2|+2|……….**

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Written by Implex

October 1, 2008 at 11:12 am

Posted in Algebra, Problem of the week

Tagged with Algebra, Problem of the week

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That would be x.

Celebrating LifeOctober 1, 2008 at 11:25 am

hmm. A re look at the question, I’m in a quandary.

Depends on where the series ends and on the sign of x.

When x>0 and when it ends with +2 it is x+2

When x>0 and when it ends with -2 it is x

When x<0 and the series end with -2, it is |x|+2

when x<0 and the series ends with +2, it is |x|+4

Celebrating LifeOctober 1, 2008 at 11:38 am

aah!Again a silly mistake .

When x>0 and when the series ends in +2 it is x

When x>0 and ends with -2, it’s x-2

Superb effort implex. Keep ’em coming!

Celebrating LifeOctober 1, 2008 at 11:52 am

It can also have two additional values, 0 and 2 when x=2.

riyaziqOctober 1, 2008 at 12:10 pm

x or x-2

4-x ,2-x

VarunOctober 1, 2008 at 1:26 pm

@Riyaziq

All the cases fall into only those four categories. Even for 2.

Celebrating LifeOctober 1, 2008 at 1:52 pm

None of the solutions have been sastisfactory

Let |x-2|=y y>=0

after every even number of mods we will again get y ( as y+2 will be positive as y is so )

now if the series ends at +2

answer will be y+2 means |x-2|+2

if the series ends at -2

we will get y or |x-2|

The solution ends here, there is no need to do anything else

all the solutions will come in the ambit of this !

Cheers !

outtimedOctober 1, 2008 at 2:30 pm

for x>=2 and

even no. of mods…ans=’x’

odd no. of mods…ans=’x-2′

for x<2 and

even no. of mods…ans=’2-x’

odd no. of mods…ans=’4-x’

wolverineOctober 1, 2008 at 5:32 pm

i think my soln…coincides with varun…[;)]

wolverineOctober 1, 2008 at 5:33 pm