Problem Solving (PS) | Re: If a+b=x and a-b= y

We can square each equation:

(a + b)^2 = x^2

a^2 + b^2 + 2ab = x^2 [Eq. 1]

and

(a - b)^2 = y^2

a^2 + b^2 - 2ab = y^2 [Eq. 2]

Now if we subtract Eq. 2 from Eq. 1, we have:

4ab = x^2 - y^2

2ab = (x^2 - y^2)/2

Alternative solution:

We are given that a + b = x and a - b = y. If we add the two equations, we have 2a = x + y or a = (x + y)/2. Similarly, if we subtract the two equations, we have 2b = x - y or
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