clock60 wrote:hi all
need help solving below problem
what is the product of all solutions of x^2+4x+7=|x+2|+3
a)-6
b)-2
c)2
d)6
e)12
oa is -6
what is out of my understanding is that, then x+2>0 x>-2 we have x=-2,-1, but only possible solution x=-1
then x+2<0, x<-2 possible x are -2.-3 and x=-3 the only solution
so product=(-1)*(-3)=3 and i have no this answer, and i cant spot my mistake
need help
Hi Guys, I wanted to chime in to bridge a concept gap I sensed.
@ clock60, your initial take on the question was correct except that you reckoned without one additional condition.
While working on problems involving absolute values, it is essential to bear the following conditions in mind:
|x+2| = x+2, if x>-2
-x-2, if x<-2
0, if x=-2
Likewise, the question shall be addressed along all these possible conditions.
x^2+4x+7=|x+2|+3
Case 1: If x>-2,
x^2 + 4x + 7 = x + 2 + 3
Solving this shall give you x = -2 or x = -1
However, the condition we are working with necessitates that an 'x' value be greater than -2; thus the only valid answer is
-1.
Case 2: If x<-2,
x^2 + 4x + 7 = -x -2 + 3
Solving this shall give you x = -2 or x = -3
With similar reasoning, x = -2 is not a valid answer as the condition requires the value be less than -2. So the only answer here is
-3
Case 3: If x = 2,
x^2 + 4x + 7 = 0 + 3
x^2 + 4x + 7 -3 =0
Solving this gives you x = -2
So, here the value of x is in line with the condition we're working with. As such, a valid answer in this case is
-2
Finally, the product of the three valid solutions is -6 [ -1 * -3 * -2]
The concept presented above addresses, maybe, one of the commonest errors test takers commit in the GMAT.
Hope that helps.
