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Find the number of real solutions of the equation x^2 - 2|x| - 8 = 0.

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Find the number of real solutions of the equation x^2 - 2|x| - 8 = 0.  [#permalink]

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New post Updated on: 14 Aug 2019, 02:11
4
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

51% (01:24) correct 49% (01:17) wrong based on 83 sessions

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Find the number of real solutions of the equation x^2 - 2|x| - 8 = 0.

A. 0
B. 1
C. 2
D. 3
E. 4

Originally posted by Dillesh4096 on 05 Aug 2019, 11:34.
Last edited by Bunuel on 14 Aug 2019, 02:11, edited 2 times in total.
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Re: Find the number of real solutions of the equation x^2 - 2|x| - 8 = 0.  [#permalink]

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New post 05 Aug 2019, 11:51
3
1
x^2 -2|x| -8 =0

If x is 0 or positive, then x^2 -2x -8 =0
--> (x-4)(x+2)=0
--> x=4 (Yes) or x=-2 (No!)

If x is negative, then x^2 +2x -8 =0
--> (x+4)(x-2)=0
--> x=-4 (Yes) or x=2 (No!)

There are only two solutions:
x=-4 and x=4


Answer is (C)

Hit that +1 kudo if you like my solution

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Re: Find the number of real solutions of the equation x^2 - 2|x| - 8 = 0.  [#permalink]

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New post 14 Aug 2019, 02:08
Hey, why are -2 and +2 not considered a solution for the problem?
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Re: Find the number of real solutions of the equation x^2 - 2|x| - 8 = 0.  [#permalink]

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New post 14 Aug 2019, 02:13
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Re: Find the number of real solutions of the equation x^2 - 2|x| - 8 = 0.  [#permalink]

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New post 14 Aug 2019, 05:03
1
anuradha619 wrote:
Hey, why are -2 and +2 not considered a solution for the problem?


because they are eliminated by conditions that we apply to find solutions and to open modulus.
if we have |x| we can open modulus if we set next conditions (https://en.wikipedia.org/wiki/Absolute_value):
1. x>=0 ...
2. x<0 ...

and this conditions are stated in the solution above

If x is 0 or positive, then x^2 -2x -8 =0
--> (x-4)(x+2)=0
--> x=4 (Yes)
or
x=-2 (No!) - because x is 0 or positive

If x is negative, then x^2 +2x -8 =0
--> (x+4)(x-2)=0
--> x=-4 (Yes) or
x=2 (No!) because x is negative
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Re: Find the number of real solutions of the equation x^2 - 2|x| - 8 = 0.   [#permalink] 14 Aug 2019, 05:03
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Find the number of real solutions of the equation x^2 - 2|x| - 8 = 0.

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