SOLUTION: if x+y=2a and x-y=2b, what is the value of xy?

Question 195416: if x+y=2a and x-y=2b, what is the value of xy?
Answer by anantha(86) (Show Source): You can put this solution on YOUR website!
sol:
x+y=2a
x-y=2b
adding these two equations
x+y=2a
x-y=2b
-----------
2x+0y=2a+2b
2x=2(a+b)
dividing by 2 on both sides we get
2x/2=2(a+b)/2
x=a+b
substitute this value in equation 1
(a+b)+y=2a
a+b+y=2a
subtracting a on both sides
a+b+y-a=2a-a
b+y=a
y=a-b(i.e;subtract b on both sides)
xy=(a+b)(a-b)
xy=a^2-b^2(i.e;(a+b)(a-b)=a*a-a*b+b*a-b*b=a^2-ab+ab-b^2=a^2-b^2)

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