Problem Solving

Methods and Strategies

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

Incorrect..OA is -6

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.

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!

-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)

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.

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