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Mod roots PS

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Mod roots PS [#permalink]  24 Jul 2010, 02:46
How many roots does the following equation have?

|| x +2 | - 2 | = 2

can some one explain how to do this algebraically

OA is 3 roots
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Re: Mod roots PS [#permalink]  24 Jul 2010, 03:26
I think it shud go like this -->

|| x +2 | - 2 | = 2 , from this take off the outermost || sign .
This will result in the following two equations :

|x+2| -2 = 2 -- 1)
and |x+2|- 2 = -2 -- 2)

Now take 1) and solve it as |x+2| = 4
Again take the || off to get
x+2 = 4 ... 3)
and x=2 = -4 ... 4)

Solve 3) to get x = 2 and solve 4) to get x = -6

Also solve 2) to get
|x+2 | = 0 , this gives us x=-2

So u have 3 values --> x= 2, -2, -6 as the 3 roots of the equation.
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Re: Mod roots PS [#permalink]  24 Jul 2010, 08:30
|| x +2 | - 2 | = 2 two cases are possible

1. | x+2 | = 0 which is only possible when x= -2

2. | x+2 | = 4 => x+2 = 4 or x+2 = -4

=> x = 2 or x = -6
hence total 3 solutions
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Re: Mod roots PS [#permalink]  20 Dec 2012, 21:19
rxs0005 wrote:
How many roots does the following equation have?
|| x +2 | - 2 | = 2

Let |x+2| = y...

$$|y-2|=2$$
$$y-2=2$$ and $$-y+2=2$$
$$y=4$$ and $$y=0$$

y=|x+2|=4
$$|x+2|=4$$
$$x+2=4$$ and $$-x-2=4$$
$$x=-2$$ and $$x=-6$$ 2 Roots!

y=|x+2|=0
What value of x has 0 distance from -2? Only the number itself! 1 Root!

Answer: 3 Roots!
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Re: Mod roots PS   [#permalink] 20 Dec 2012, 21:19
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