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Re: Which of the following is always equal to sqrt (9+x^2-6x)? [#permalink ]
19 Feb 2013, 04:09
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Re: Which of the following is always equal to sqrt (9+x^2-6x)? [#permalink ]
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 ]
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 ]
21 Feb 2013, 02:28

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Re: Which of the following is always equal to sqrt(9+x^2-6x)? [#permalink ]
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 ]
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 ]
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 ]
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 ]
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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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 ]
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| = 93,9 Let's plug 6, -6 into the answer choices: C.) |3 - x| |3 - 6| = 3 |3- (-6)| = 93,9 (C)

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