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# Signs of roots

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Director
Joined: 02 Sep 2016
Posts: 682

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15 Nov 2017, 10:26
If we write

x^2= 4

Then there are two possible values 2 and -2.

But does squaring both sides make any difference?

x= root 4= +2 and no negative.
Board of Directors
Joined: 17 Jul 2014
Posts: 2621
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)

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15 Nov 2017, 14:45
if you put everything under a square root, you eliminate one option...
there's no way for a negative number to be under square root...
a square root undoes the operation of squaring. any number, positive or negative, squared is a positive one.

if you write sqrt(|x|^2), then it's fine, otherwise, you miss 50% of the solutions for the question.
Math Expert
Joined: 02 Sep 2009
Posts: 51102

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15 Nov 2017, 20:04
Shiv2016 wrote:
If we write

x^2= 4

Then there are two possible values 2 and -2.

But does squaring both sides make any difference?

x= root 4= +2 and no negative.

The point is that $$\sqrt{x^2}=|x|$$.

$$x^2 = 4$$;

$$|x|=\sqrt{4}$$;

$$x=\sqrt{4}$$ or $$x = -\sqrt{4}$$.

Hope it's clear.
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Re: Signs of roots &nbs [#permalink] 15 Nov 2017, 20:04
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