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Which of the following is always equal to √(9 + x^2 -6x) ?

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by vinni.k » Sat Jan 11, 2014 8:33 am
Which of the following is always equal to √(9 + x^2 -6x) ?
A.x -3
B.3 + x
C.|3 - x|
D.|3 +x|
E.3 - x

OA is C

Please help on this one. I don't feel this question is correct because after factorization it gives
√(x-3)^2 that is equal to |x - 3| i.e √(x-3)^2 = |x - 3|

So, what is X here positive or negative.
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by theCodeToGMAT » Sat Jan 11, 2014 7:50 pm
√(9 + x^2 -6x)

it can be

sqrt(3-x)^2 = 3-x

or

sqrt(x-3)^2 = x-3

Since, |3-x| is either 3-x or x-3

{C}
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by Uva@90 » Sat Jan 11, 2014 8:01 pm
vinni.k wrote:Which of the following is always equal to √(9 + x^2 -6x) ?
A.x -3
B.3 + x
C.|3 - x|
D.|3 +x|
E.3 - x

OA is C

Please help on this one. I don't feel this question is correct because after factorization it gives
√(x-3)^2 that is equal to |x - 3| i.e √(x-3)^2 = |x - 3|

So, what is X here positive or negative.
Hi Vinni,
What you did is correct.
I assume you have confused with |x-3| and |3-x|
Both yield same values.

You ended as √(x-3)^2 = |x - 3| which is = |3-x|
hence answer is C

Regards,
Uva.
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by vinni.k » Sat Jan 11, 2014 8:07 pm
Thanks Rahul.

I am not sure how to follow you. How you got this one sqrt(3-x)^2 = 3-x ?
This is fine:- sqrt(x-3)^2 = x-3 but not sure about the above one.

Vinni
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by theCodeToGMAT » Sat Jan 11, 2014 8:16 pm
vinni.k wrote:Thanks Rahul.
I am not sure how to follow you. How you got this one sqrt(3-x)^2 = 3-x ?
This is fine:- sqrt(x-3)^2 = x-3 but not sure about the above one.
Vinni
This is because (3-x)^2 = 9 + x^2 - 6x
and
(x-3)^2 = x^2 + 9 - 6x
both blue parts are same
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by vinni.k » Sat Jan 11, 2014 8:41 pm
Uva@90 wrote: What you did is correct.
I assume you have confused with |x-3| and |3-x|
Both yield same values.

You ended as √(x-3)^2 = |x - 3| which is = |3-x|
hence answer is C

Regards,
Uva.
Thanks Uva, but can you please prove how |x - 3| is |3 - x|. I am just confused between A and C.

Vinni
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by Uva@90 » Sat Jan 11, 2014 9:09 pm
vinni.k wrote:
Uva@90 wrote: What you did is correct.
I assume you have confused with |x-3| and |3-x|
Both yield same values.

You ended as √(x-3)^2 = |x - 3| which is = |3-x|
hence answer is C

Regards,
Uva.
Thanks Uva, but can you please prove how |x - 3| is |3 - x|. I am just confused between A and C.

Vinni
Hi Vinni,
Let us consider X = 1
√(9 + x^2 -6x) =2
and |x - 3| =2 and |3 - x| is also 2

Let us consider X = -1
√(9 + x^2 -6x) =4
|x - 3| =4 and |3 - x| is also 4
I am just confused between A and C.
Let us consider simple one,
√x^2 = x when x>0
and -x when x <0

similarly,
√(9 + x^2 -6x) should have both values (x-3) and (-x+3)
Option A has only one value.
Where as C has both.

Hence Ans is C

Regards,
Uva.
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by vinni.k » Sat Jan 11, 2014 9:49 pm
Okay. I think i got your point. Clearly understandable. Thank you and really appreciate it. :D

Regards
Vinni
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by GMATGuruNY » Sun Jan 12, 2014 4:14 am
vinni.k wrote:Which of the following is always equal to √(9 + x^2 -6x) ?
A.x -3
B.3 + x
C.|3 - x|
D.|3 +x|
E.3 - x

OA is C
Let x=1.
In this case, √(9 + x² - 6x) = √4 = 2.
Now plug x=1 into the answer choices and eliminate any that don't yield a value of 2.

A. x -3 = 1-3 = -2.
B. 3 + x = 3 + 1 = 4.
C. |3 - x| = |3-1| = 2.
D. |3 +x| = |3+1| = 4.
E. 3 - x = 3-1 = 2.
Eliminate A, B and D.

Test an EXTREME value.
Let x=10.
In this case, √(9 + x² - 6x) = √49 = 7.
Now plug x=10 into the remaining answer choices and eliminate any that don't yield a value of 7.

C. |3 - x| = |3-10| = 7.
E. 3 - x = 3-10 = -7.
Eliminate E.

The correct answer is C.
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by Matt@VeritasPrep » Wed Jan 15, 2014 12:27 pm
One last (succinct) way:

√z² = |z| for any value of z.

So ...

√(x² - 6x + 9) = √(x-3)(x-3) = √(x-3)² = |x-3|.

Hence the answer is C!
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