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

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If x+y=a and x-y=b, then 2xy=? [#permalink]

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

a) \(\frac{(a^2 - b^2)}{2}\)
b) \(\frac{(b^2 - a^2)}{2}\)
c) \(\frac{(a - b )}{2}\)
d) \(\frac{(ab)}{2}\)
e) \(\frac{(a^2 + b^2)}{2}\)
Spoiler: OA
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Re: If x+y=a and x-y=b, then 2xy=? [#permalink]

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jlgdr wrote:
If x+y=a and x-y=b, then 2xy=?

a) \(\frac{(a^2 - b^2)}{2}\)
b) \(\frac{(b^2 - a^2)}{2}\)
c) \(\frac{(a - b )}{2}\)
d) \(\frac{(ab)}{2}\)
e) \(\frac{(a^2 + b^2)}{2}\)


Sum the equations: 2x = a + b;

Subtract the equations: 2y = a-b;

Multiply: 4xy = a^2 - b^2 --> 2xy = (a^2- b^2)/2.

Answer: A.
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Re: If x+y=a and x-y=b, then 2xy=? [#permalink]

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New post 28 Oct 2014, 00:59
x + y = a

\(x^2 + 2xy + y^2 = a^2\) ............. (1)

x - y = b

\(x^2 - 2xy + y^2 = b^2\) ................ (2)

(1) - (2)

\(4xy = a^2 - b^2\)

\(2xy = \frac{a^2-b^2}{2}\)

Answer = A
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If x+y=a and x-y=b, then 2xy=? [#permalink]

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New post 28 Dec 2014, 19:35
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Plug in any number..

Let x=3, y=2, then: 2xy = 2x3x2 = 12
And:
a = 3+2 = 5
b = 3-2 = 1

Now plug a=5, b=1 into the anwers choices:

A. (25-1)/2= 12 (yes!)
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Re: If x+y=a and x-y=b, then 2xy=? [#permalink]

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New post 29 Oct 2017, 07:21
Expert's post
jlgdr wrote:
If x+y=a and x-y=b, then 2xy=?

a) \(\frac{(a^2 - b^2)}{2}\)
b) \(\frac{(b^2 - a^2)}{2}\)
c) \(\frac{(a - b )}{2}\)
d) \(\frac{(ab)}{2}\)
e) \(\frac{(a^2 + b^2)}{2}\)


Squaring the first equation, we have:

x^2 + 2xy + y^2 = a^2

Squaring the second equation, we have:

x^2 - 2xy + y^2 = b^2

Subtracting the second equation from the first, we have:

4xy = a^2 - b^2

2xy = (a^2 - b^2)/2

Answer: A
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Re: If x+y=a and x-y=b, then 2xy=?   [#permalink] 29 Oct 2017, 07:21
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