Question

(x-y) = 12 and xy = 25/4
find (x + y)

Answer 1

x - y = 12
squaring on both sides
x^2 + y^2 - 2xy = 144

Adding 4xy to this equation on both sides

x^2 + y^2 - 2xy + 4xy = 144 + 4xy

we already know that xy = 25/4

Then x^2 + y^2 + 2xy = 144 + 4 * 25/4 = 144 + 25 = 169

but x^2 + y^2 + 2xy = (x +y)^2

thus (x + y)^2 = 169
==> x + y = 13.

Answer 2

see hope you will understand