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Why is square root of (x-1)^2 not...

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Senior | Next Rank: 100 Posts
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by anniev2 » Sat Mar 14, 2009 9:17 am
OG 11 # 171

If (x-1)^2 = 400, which of the following could be the value of x-5?

(A) 15
(B) 14
(C) -24
(D) -25
(E) -26

OA is C


Why is square root of (x-1)^2 not equal to -(x-1) and (x-1). I thought that taking the square root of a number means its +/- the number. Please advise.
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by cramya » Sat Mar 14, 2009 9:28 am
Know this: Square root of x^2 = |x|

(x-1) ^ 2 = 400

|x-1| = 20

Case 1: x is positive

x-1 = 20
x=21

Case 2: x is negative

-(x-1)= 20

-x+1 = 20

x=-19




x-1 could have equaled 21 or -19

(21-1)^2 = 400 and (-19-1)^2 = 400


-19-5= -24 -> the only choice given since 21-5 = 16 is not one of the choices

Hence C

Regards,
CR
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Re: Why is square root of (x-1)^2 not...

by logitech » Sat Mar 14, 2009 9:28 am
well this problem is like:
'
X^2=400 and the two cases you need to consider is on the right side of the equation:

+20 and - 20

I am sure you can solve the question now.
LGTCH
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