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What is the product of all the solutions of (x + 2)^2 = |x + 2|? 17 May 2024, 09:28
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If the LHS is a square value, does that not mean the RHS can only be positive?
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What is the product of all the solutions of (x + 2)^2 = |x + 2|? 17 May 2024, 09:39
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mollyweasley
If the LHS is a square value, does that not mean the RHS can only be positive?
­Positive or zero, but x itself could be negative
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What is the product of all the solutions of (x + 2)^2 = |x + 2|? 17 May 2024, 10:21
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(x+2)²=|x+2|
Squaring both sides
(X+2)⁴=(x+2)²
Let (x+2)²=t
t²-t=0
t(t-1)=0
t=0,t=1
(X+2)²=0,x=-2
(X+2)²=1,x=+-1-2
X=-1 and -3
Product=-6 ans

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What is the product of all the solutions of (x + 2)^2 = |x + 2|? 24 May 2024, 12:10
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­Replace x+2 with t 

t^2 = |t|
t^2 - |t| = 0
t = 0      t =+-1
x+2 = 0            x+2 = 1        x+2 = -1

x = -2                  x = -1               x = -3

           Product = -6
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What is the product of all the solutions of (x + 2)^2 = |x + 2|? 25 May 2024, 06:51
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Bunuel
What is the product of all the solutions of (x + 2)^2 = |x + 2|?

A. -6
B. -2
C. 2
D. 6
E. 12
­Let, x+2 = a

then (x + 2)^2 = |x + 2| becomes \(a^2 = |a|\) which is possible for

a = ±1 OR a = 0
i.e x+2 = ±1 OR x+2 = 0

if x+2 = 1 then x = -1
if x+2 = -1 then x = -3
if x+2 = 0 then x = -2

Product of all possible values of x = (-1)*(-3)*(-2) = -6

Answer: Option A


­
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What is the product of all the solutions of (x + 2)^2 = |x + 2|? 05 Jun 2024, 11:27
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First let's understand this, as LHS = RHS.
Both has to be equal so there are only three possibilities i.e put -1, -2, -3.
And other than these LHS will not be equal to RHS.
So ans would be -1*-2*-3 =-6

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What is the product of all the solutions of (x + 2)^2 = |x + 2|? 22 Jun 2024, 03:36
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Bunuel
What is the product of all the solutions of (x + 2)^2 = |x + 2|?

A. -6
B. -2
C. 2
D. 6
E. 12
­
Keep in mind:

\((x+2)^2 = |x+2|^2\)

Hence we can write the given equation as:\(|x+2|^2 - |x+2| = 0 \)

\(|x+2| * ( |x+2| - 1) = 0\)

So either |x+2| = 0 which means x = -2
or
|x+2| - 1 = 0 which means x is -1 or -3

Product of all solutions = -1 * -2 * -3 = -6

Answer (A)­

Video on solving absolute values:
https://youtu.be/oqVfKQBcnrs
 
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What is the product of all the solutions of (x + 2)^2 = |x + 2|? 04 Aug 2024, 00:52
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What is the product of all the solutions of (x + 2)^2 = |x + 2|? 13 Aug 2024, 10:22
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Bunuel
What is the product of all the solutions of (x + 2)^2 = |x + 2|?

A. -6
B. -2
C. 2
D. 6
E. 12
­Here's an easy and quick approach to doing this problem:

We are asked for the product of the solutions, thus the factors of the right option will be the solutions.

It is easy to work with the options given. Say, at random you start off with 12 - Factors of twelve can be written in pairs as follows:
(1,12),(2,6),(3,4) - and negative pairs of the same. Test them out and you will find that they don't work in the given equation.

Do the same for -6, and you'll have both 3 & -2 working. I managed to do this in a flat 25 seconds this way. I found it faster to substitute and do the calcs in my head than to sit and go through the algebra of it.
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What is the product of all the solutions of (x + 2)^2 = |x + 2|? 16 Dec 2024, 16:37
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O great Bunuel, the math genius, do you have any similar problems for practice?
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What is the product of all the solutions of (x + 2)^2 = |x + 2|? 17 Dec 2024, 00:04
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braddouglas10
O great Bunuel, the math genius, do you have any similar problems for practice?

Check absolute value questions here: https://gmatclub.com/forum/search.php?s ... &tag_id=58
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What is the product of all the solutions of (x + 2)^2 = |x + 2|? 21 Dec 2024, 16:50
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Thank you, great Bunuel, the math genius!
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braddouglas10
O great Bunuel, the math genius, do you have any similar problems for practice?

Check absolute value questions here: https://gmatclub.com/forum/search.php?s ... &tag_id=58
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