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Source: — Problem Solving |
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by vittalgmat » Fri Oct 03, 2008 6:30 pm
The answer is 12
here is how

|x +2| has 2 solutions: +(x+2) and -(x+2)
using this we get 2 equations

1) x^2 +4x +7 = x +2 +3

2) x^2 +4x +7 = -x -2 +3

Solving these two equations we get the following roots
-3, -2, -2 -1. Their product is 12
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by dferm » Fri Oct 03, 2008 6:55 pm
Incorrect..OA is -6
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by krazy800 » Fri Oct 03, 2008 9:41 pm
The solution x=-2 is common whether u consider -(X+2) or (X+2)..

There fore u got 2 consider the product of -3,-2,-1 only and not -3,-2,-2 and -1..

This will give u right answer -6.
Aiming High
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by cramya » Fri Oct 03, 2008 9:45 pm
3, -2, -2 -1

Vittal, I think we just have to take the disttinct solutions and multiply i.e
-3,-2 and -1 and the product is -6 (since -2 is a solution eve though we get it from both equations)

Nice problem!
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by cramya » Fri Oct 03, 2008 9:47 pm
-3, -2, -2 -1

Vittal, I think we just have to take the disttinct solutions and multiply i.e
-3,-2 and -1 and the product is -6 (since -2 is a solution we should not include it twice even though we get it from both equations)
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by vittalgmat » Sun Oct 05, 2008 9:23 am
Thanks.. but I am still not convinced.. the Problem said product of "ALL" solutions instead of product of "distinct" solutions.

Does my argument makes sense??


pls let me know ur thoughts.
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by mental » Mon Oct 06, 2008 2:59 am
Vittal since the solutions are from only one equation, we will consider -2 only once

lets take (x+2)^2=0
this equation has only one unique solution: x = -2

but it can also be written as (x + 2)(x + 2)=0
with each component simplifying to (x + 2) =0, giving same answer
we dont consider it twice, but only once
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