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by Rahul@gurome » Thu Aug 12, 2010 3:02 pm
Jinglander wrote:x+y=a and
x-y=b

what is 2xy

answer is

(a^2-b^2)/2

How do you solve this by alg
x+y=a implies (x + y)^2 = a^2 or x^2 + y^2 + 2xy = a^2...Equation (1)
x - y=b implies (x - y)^2 = b^2 or x^2 + y^2 - 2xy = b^2...Equation (2)
Subtract Equations (1) and (2) above, 4xy = a^2 - b^2
or 2(2xy) = a^2 - b^2

or 2xy = (a^2-b^2)/2
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by nithi_mystics » Thu Aug 12, 2010 3:03 pm
x+y = a

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

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

a^2 - b^2 = 4xy

==> 2xy = (a^2 - b^2)/2
Thanks
Nithi