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faster way to solve Algebra problem??

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Source: — Problem Solving |
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by stop@800 » Mon Sep 22, 2008 7:27 am
(a+b)^2 = a^2 + b^2 + 2ab
(a-b)^2 = a^2 + b^2 - 2ab

(a+b)^2 - (a-b)^2 = 4ab
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by tendays2go » Mon Sep 22, 2008 7:33 am
Also,

(x+y)^2 - (x-y)^2 = 2xy + 2xy =4xy
thus, 4xy => a^2 -b^2
i.e. 2xy = (a^2 - b^2)/2
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by smallsorrow » Mon Sep 22, 2008 7:36 am
Wow - you guys surely get an 800!!
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by smithpa2 » Mon Sep 22, 2008 7:38 am
You could plug in some numbers., for example, x=3 y=2
x+y=a or 3+2=5 and x-y=b or 3-2=1.

Then 2xy=2*3*2= 12 and a^2-b^2/2 = (25-1)/2=12
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by gmat579 » Mon Sep 22, 2008 1:16 pm
x + y = a ---- 1
x - y = b -----2

Adding equations 1 and 2

2x = a + b ---- 3

Subtracting 2 from 1

2y = a - b ----- 4

Multiplying eq.3 and eq.4 ...

4xy = (a+b)(a-b)

Dividing by 2...

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