Question

find x and y ??????!!!!

Answer 1

Given:
     (a+b) x + (a-b) y = a² + b²    --- (1)
     (a - b) x + ( a + b) y = a² + b²   --- (2)

Multiply (1) by (a+b) and Multiply (2) by (a-b) and subtract. This eliminates the variable y.  We multiply like above to make the coefficients of "y" equal in both equations.

(a+b)² x + (a² - b²) y - (a-b)² x - (a² - b²) y = (a²+b²) (a+b) - (a²+b²)(a-b)

       4 a b x = 2 b (a²+b²)
       x = (a²+b²)/2a

Substitute this value of x in (1) to get:
      (a+b) (a²+b²)/2a  + (a-b) y = a²+b²
      (a-b) y = (a²+b²) * [ 2a - a - b] /2a
            y = (a²+b²)/2a
Assume that a ≠ b, for canceling the factor (a-b) on both sides.

   If a = b, then also  x = y = (a²+b²)/2a = a = b