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

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Re: Which of the following is always equal to sqrt (9+x^2-6x)? [#permalink] New post 19 Feb 2013, 04:09
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Sachin9 wrote:
This is true and absolute value properties confirms this because:
|a-b| = |b-a|


Bunuel/KArishma,
Is this always true?


Yes, since both |a-b| and |b-a| represent the distance between a and b on the number line.

COMPLETE SOLUTION:

Which of the following is always equal to \sqrt{9+x^2-6x}?
A. x - 3
B. 3 + x
C. |3 - x|
D. |3 + x|
E. 3 - x

\sqrt{9+x^2-6x}=\sqrt{(3-x)^2}=|3-x|.

Answer: C.
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Re: Which of the following is always equal to sqrt (9+x^2-6x)? [#permalink] New post 19 Feb 2013, 05:16
Bunuel wrote:
Sachin9 wrote:
This is true and absolute value properties confirms this because:
|a-b| = |b-a|


Bunuel/KArishma,
Is this always true?


Yes, since both |a-b| and |b-a| represent the distance between a and b on the number line.

COMPLETE SOLUTION:

Which of the following is always equal to \sqrt{9+x^2-6x}?
A. x - 3
B. 3 + x
C. |3 - x|
D. |3 + x|
E. 3 - x

\sqrt{9+x^2-6x}=\sqrt{(3-x)^2}=|3-x|.

Answer: C.


amazing, I dont know why I fail/forget to consider |a-b| as the distance between a and b. I repeatedly commit this mistake..
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Re: Which of the following is always equal to sqrt(9+x^2-6x)? [#permalink] New post 20 Feb 2013, 20:31
Which of the following is always equal to \sqrt{9+x^2-6x}?

A. x - 3
B. 3 + x
C. |3 - x|
D. |3 + x|
E. 3 - x


Hi, can anyone explain me how to go abt this...the above answers have got a
lil confusing for me.

ill go one option at a time:

A. x-3

when we square x-3 it give x^2+9-6x
if we squareroot x^2+9-6x then we get the same exp...so for me this seems
to be an answer

B. 3+x

when we square 3+x it gives 9+6x+x^2
this is all positive unlike 9+x^2-6x given in the question, so not an answer

C. |3-x|

given sqrt{9+x^2-6x}

solving sqrt(3-x)

|3-x|=sqrt(3-x)

this too seems to be a possible answer

D. |3+x|

this will give 9+x^2+6x which is not equal to the equation given hence not
an answer

E. 3-x

=9+x^2-6x

this too seems fine

can anyone please clarify where im going wrong.... in all the options...


Thanks
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Re: Which of the following is always equal to sqrt(9+x^2-6x)? [#permalink] New post 21 Feb 2013, 02:28
Expert's post
mehasingh wrote:
Which of the following is always equal to \sqrt{9+x^2-6x}?

A. x - 3
B. 3 + x
C. |3 - x|
D. |3 + x|
E. 3 - x


Hi, can anyone explain me how to go abt this...the above answers have got a
lil confusing for me.

ill go one option at a time:

A. x-3


Notice that the square root function cannot give negative result: \sqrt{{some \ expression}}\geq{0}.

So, \sqrt{9+x^2-6x}=\sqrt{(3-x)^2}\geq{0}.

Now, in option A we have x-3, which can be negative if x<3, so A cannot be the correct answer.

Hope it's clear.
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Re: Which of the following is always equal to sqrt(9+x^2-6x)? [#permalink] New post 24 Mar 2013, 10:11
sqrt (9+x^2-6x) = sqrt( (3-x)^2 )
= |3-x|

sqrt (9+x^2-6x) = sqrt( (x-3)^2 )
= |x-3|

but we have only |3-x| as option, so "C"
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Re: Which of the following is always equal to sqrt(9+x^2-6x)? [#permalink] New post 13 Apr 2013, 05:51
From the property |X| = sqrt( X^2 )

| 3 - X | = sqrt ( (3 - X)^2 )
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Re: Which of the following is always equal to sqrt(9+x^2-6x)? [#permalink] New post 13 Apr 2013, 10:46
GK_Gmat wrote:
Which of the following is always equal to \sqrt{9+x^2-6x}?

A. x - 3
B. 3 + x
C. |3 - x|
D. |3 + x|
E. 3 - x


x^2 - 6x+9 = (3-x)^2 thus\sqrt{9+x^2-6x} = x-3 or 3-x this is equivel to /3-x/
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Re: Which of the following is always equal to sqrt(9+x^2-6x)? [#permalink] New post 15 Jun 2013, 08:57
I originally said (x-3) was the right answer.

In essence, this is a "square root of a square" problem, is it not? In that case, isn't the result always a positive number?
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Re: Which of the following is always equal to sqrt(9+x^2-6x)? [#permalink] New post 15 Jun 2013, 09:02
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WholeLottaLove wrote:
I originally said (x-3) was the right answer.

In essence, this is a "square root of a square" problem, is it not? In that case, isn't the result always a positive number?


Whenever you have an expression in the form \sqrt{x^2} it becomes |x|.
So in this case \sqrt{(x-3)^2}=|x-3|

For example if \sqrt{x^2}=3 x could be 3 and \sqrt{3^2}=3
but could also be -3 as \sqrt{(-3)^2}=3.

That's why we need the abs value x=|3|
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Re: [#permalink] New post 15 Jun 2013, 12:19
bkk145 wrote:
The answer is indeed
|x-3|

Don't for get that...

|x-3| = |3-x|

C is the answer.


excellent, thank you for the help.
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Re: Which of the following is always equal to sqrt(9+x^2-6x)? [#permalink] New post 01 Jul 2013, 10:13
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

√(9+x^2-6x)
√(x^2 - 6x + 9)
√(x - 3)*(x - 3)
√(x - 3)^2
|x - 3| (Square root of a square...)

Lets choose two values for x: 6, -6
|6-3| = 3
|-6-3| = 9
3,9

Let's plug 6, -6 into the answer choices:

C.) |3 - x|
|3 - 6| = 3
|3- (-6)| = 9
3,9

(C)
Re: Which of the following is always equal to sqrt(9+x^2-6x)?   [#permalink] 01 Jul 2013, 10:13
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