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OG Pg 186 Problem 245

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OG Pg 186 Problem 245 [#permalink] New post 18 Jan 2009, 12:07
Ok so I feel stupid asking this but i am having a problem at a certain point in the problem:

If x+y=a and x-y=b then 2xy= ?

The answer is: 2xy= (a^2 - b^2)/2

I got it to this:

y= [2a/2] - [(a+b)/2]

why is the numerator then in the next step: 2a-a-b and not 2a-a+b?

Thanks!
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Re: OG Pg 186 Problem 245 [#permalink] New post 18 Jan 2009, 14:00
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hardaway7 wrote:
Ok so I feel stupid asking this but i am having a problem at a certain point in the problem:

If x+y=a and x-y=b then 2xy= ?

The answer is: 2xy= (a^2 - b^2)/2

I got it to this:

y= [2a/2] - [(a+b)/2]

why is the numerator then in the next step: 2a-a-b and not 2a-a+b?

Thanks!


hardaway, when you post the question, you don't need to post page number and problem number from OG. Just copy the question w/ all the choices.

To answer your question.

(x+y)^2 = x^2 + 2xy + y^2
(x-y)^2 = x^2 - 2xy + y^2

we know that:
a^2 = (x+y)^2
b^2 = (x-y)^2

so,
a^2 - b^2 = (x^2 + 2xy + y^2) - (x^2 - 2xy + y^2)
= x^2 - x^2 + 2xy + 2xy + y^2 - y^2
= 4xy

4xy = a^2 - b^2
2xy = (a^2 - b^2)/2
Re: OG Pg 186 Problem 245   [#permalink] 18 Jan 2009, 14:00
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OG Pg 186 Problem 245

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