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by parallel_chase » Tue Aug 05, 2008 3:54 pm
if you look closely x² – 2xy + y² – 9 = 0 can be simplified as (x-y)^2 =9

Rest is just a cake walk.

x-y = 3
x+y=15

2x=18
x=9
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by sibbineni » Tue Aug 05, 2008 7:43 pm
If x > y, x² – 2xy + y² – 9 = 0 and x + y = 15, what is x?

(x² – 2xy + y²)-9=0

(x² – 2xy + y²) is of the form (x-y)^2

i.e (a-b)^2=a^2-2ab+b^2

so (x-y)^2=9

x-y=+/- 3

but as x>y

x-y=3--(1)
x+y=15---(2)

solve for x

x+x-3=15

2x=18

x=9
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by jimmytwoshoes » Thu Aug 07, 2008 3:57 pm
Couldn't you also say that because x>y and x+y=15 that x has to be at least 7.5, and e is the only one greater than 7.5?
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by *arch* » Thu Aug 07, 2008 7:04 pm
An even simpler way would be to look at the answer choices.

We have a condition x>y that must be satisfied in the equation x+y = 15.

Only option (E) where x = 9 satisfies this condition. In all other options (A), (B), (C) & (D), x will be less than y which violates the condition stated in the question. :D
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by gmat_novice » Thu Aug 07, 2008 8:30 pm
Excellent solution "Arch"! :D
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by luiscarlos59 » Sun Jun 05, 2011 4:10 pm
I have a question regarding the point where you get
(x-y) = +/- 3

While using the crtieria of x>y , i dont understand why to chose the

x-y = +3 and not x-y= -3 ?

If x is greater than y , you could get -3 as an answer also.
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by cans » Sun Jun 05, 2011 4:17 pm
luiscarlos59 wrote:I have a question regarding the point where you get
(x-y) = +/- 3

While using the crtieria of x>y , i dont understand why to chose the

x-y = +3 and not x-y= -3 ?

If x is greater than y , you could get -3 as an answer also.
x>y means x-y>0 but -3 is not greater than 0. Thus we can't get -3 as an answer.
If my post helped you- let me know by pushing the thanks button ;)

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by aftableo2006 » Sun Jun 05, 2011 11:01 pm
x=9 is the answer since x>y so x-y=3 and x+y=15
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by smackmartine » Sun Jun 05, 2011 11:12 pm
luiscarlos59 wrote:I have a question regarding the point where you get
(x-y) = +/- 3

While using the crtieria of x>y , i dont understand why to chose the

x-y = +3 and not x-y= -3 ?


If x is greater than y , you could get -3 as an answer also.
If you take x-y= -3 , and solve x-y = -3 & x+y=15 , you will get:

x=6 , and y = 9 ,but its given that x>y , So you cannot take x-y = -3

Solving x-y = 3 & x+y=15, we get x=9 , y= 6
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by krishnasty » Sun Jun 05, 2011 11:19 pm
*arch* wrote:An even simpler way would be to look at the answer choices.

We have a condition x>y that must be satisfied in the equation x+y = 15.

Only option (E) where x = 9 satisfies this condition. In all other options (A), (B), (C) & (D), x will be less than y which violates the condition stated in the question. :D
excellent answer arch..
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