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Re: Which of the following is always equal to sqrt (9+x^26x)? [#permalink]
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19 Feb 2013, 05:09
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Re: Which of the following is always equal to sqrt (9+x^26x)? [#permalink]
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19 Feb 2013, 06:16
Bunuel wrote: Sachin9 wrote: This is true and absolute value properties confirms this because: ab = ba
Bunuel/KArishma, Is this always true? Yes, since both ab and ba represent the distance between a and b on the number line. COMPLETE SOLUTION: Which of the following is always equal to \(\sqrt{9+x^26x}\)?A. x  3 B. 3 + x C. 3  x D. 3 + x E. 3  x \(\sqrt{9+x^26x}=\sqrt{(3x)^2}=3x\). Answer: C. amazing, I dont know why I fail/forget to consider ab 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^26x)? [#permalink]
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20 Feb 2013, 21:31
Which of the following is always equal to \sqrt{9+x^26x}?
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. x3
when we square x3 it give x^2+96x if we squareroot x^2+96x 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^26x given in the question, so not an answer
C. 3x
given sqrt{9+x^26x}
solving sqrt(3x)
3x=sqrt(3x)
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. 3x
=9+x^26x
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^26x)? [#permalink]
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21 Feb 2013, 03:28



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Re: Which of the following is always equal to sqrt(9+x^26x)? [#permalink]
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24 Mar 2013, 11:11
sqrt (9+x^26x) = sqrt( (3x)^2 ) = 3x
sqrt (9+x^26x) = sqrt( (x3)^2 ) = x3
but we have only 3x as option, so "C"



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Re: Which of the following is always equal to sqrt(9+x^26x)? [#permalink]
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13 Apr 2013, 06:51
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^26x)? [#permalink]
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13 Apr 2013, 11:46
GK_Gmat wrote: Which of the following is always equal to \(\sqrt{9+x^26x}\)?
A. x  3 B. 3 + x C. 3  x D. 3 + x E. 3  x x^2  6x+9 = (3x)^2 thus\(\sqrt{9+x^26x}\) = x3 or 3x this is equivel to /3x/



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Re: Which of the following is always equal to sqrt(9+x^26x)? [#permalink]
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15 Jun 2013, 09:57
I originally said (x3) 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^26x)? [#permalink]
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15 Jun 2013, 10:02
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WholeLottaLove wrote: I originally said (x3) 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 \(\sqrt{(x3)^2}=x3\) 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 x3
Don't for get that...
x3 = 3x
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^26x)? [#permalink]
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01 Jul 2013, 11:13
Which of the following is always equal to √(9+x^26x)?
A. x  3 B. 3 + x C. 3  x D. 3 + x E. 3  x
√(9+x^26x) √(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 63 = 3 63 = 9 3,9
Let's plug 6, 6 into the answer choices:
C.) 3  x 3  6 = 3 3 (6) = 9 3,9
(C)



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Re: Which of the following is always equal to sqrt(9+x^26x)? [#permalink]
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Re: Which of the following is always equal to sqrt(9+x^26x)? [#permalink]
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26 Dec 2014, 11:21
Answer to this question is +/ (x3) both,but we need to define the range of x because Domain y is always positive i.e.above xaxis. So, for x>3 y=(x3) and for x<3, y=(3x) It can be rewritten as x3 or 3  x ............. which is in agreement with property of modulus ie xa=ax Ideally one must always remember that Sqrt(xa)^2 = xa and, xa= xa , if x>a = (xa) , if x<a. Hope, it makes sense . GK_Gmat wrote: Which of the following is always equal to \(\sqrt{9+x^26x}\)?
A. x  3 B. 3 + x C. 3  x D. 3 + x E. 3  x
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Re: Which of the following is always equal to sqrt(9+x^26x)? [#permalink]
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07 Apr 2015, 10:36
Bunuel Can you please help here? According to my understanding there are two cases in the GMAT: Case 1 : sqrt[(5)*(5)] = 5 Case 2 : sqrt[(5)*(5)] = 5 Is my understanding correct? Thanks in advance Ankit
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Re: Which of the following is always equal to sqrt(9+x^26x)? [#permalink]
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07 Apr 2015, 10:48
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ankittiss wrote: Bunuel Can you please help here? According to my understanding there are two cases in the GMAT: Case 1 : sqrt[(5)*(5)] = 5 Case 2 : sqrt[(5)*(5)] = 5 Is my understanding correct? Thanks in advance Ankit No, it's totally wrong. When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is: \(\sqrt{9} = 3\), NOT +3 or 3; \(\sqrt[4]{16} = 2\), NOT +2 or 2; Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and 3. Because \(x^2 = 9\) means that \(x =\sqrt{9}=3\) or \(x=\sqrt{9}=3\). About \(\sqrt{x^2}=x\): Again, the point here is that since square root function can not give negative result then \(\sqrt{some \ expression}\geq{0}\). So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to? Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\). So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). What function does exactly the same thing? The absolute value function: \(x=x\), if \(x\geq{0}\) and \(x=x\), if \(x<0\). That is why \(\sqrt{x^2}=x\). Hope it helps.
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Re: Which of the following is always equal to sqrt(9+x^26x)? [#permalink]
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07 Apr 2015, 11:51
Thanks BunuelThat really helps
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Re: Which of the following is always equal to sqrt(9+x^26x)? [#permalink]
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Re: Which of the following is always equal to sqrt(9+x^26x)? [#permalink]
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25 Jul 2016, 02:39
GK_Gmat wrote: Which of the following is always equal to \(\sqrt{9+x^26x}\)?
A. x  3 B. 3 + x C. 3  x D. 3 + x E. 3  x There should be no confusion regarding this question. SQUAREROOT and MODULUS have the same property regarding the polarity of a number. THEY BOTH YIELDS ONLY POSITIVE OUTPUTS. Q: what is the surest way to make any value positive. ? A: Take the modulus of the value x So we know \(\sqrt{9+x^26x}\) will gives us ONLY POSITIVE VALUE, Then we should make sure that the option also matches this property. Therefore only 3  x and 3+x are the one that will always give positive value BUT 3+x is not a root or solution of \(\sqrt{9+x^26x}\) So the only option left is 3x ANSWER IS C
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