Question

( a+b ) x + ( a-b ) y = 2a.
( a-b ) x + ( a+b ) y = 2b.

solve this equation using multiplication method

Ans it ASAP

Answer 1

Given   (a-b)x+(a+b)y = 2a2+2b2 ------------(1), (a+b)x-(a-b)y = 4ab -----------(2)
multiply (a+b) in equation (1) and (a-b) in equation (2) we get
(a-b)(a+b)x + (a+b)2y = 2(a2+b2 )(a+b)
(a-b)(a+b)x -  (a-b)2y = 4ab(a-b)         (substract)       
---------------------------------------------------------
                2(a2+b2 )y = 2a3 +2a2b+2ab2+2b3 -4a2b+4ab2
                            y = (2a3 +2b3 -2a2b+6ab2 ) / 2(a2+b2 )
                            y = 2(a3 +b3 -a2b+3ab2 ) / 2(a2+b2 )
                            y = (a3 +b3 -a2b+3ab2 ) / (a2+b2 )
multiply (a-b) in equation (1) and (a+b) in equation (2) we get
     (a-b)2x + (a+b)(a-b)y = 2(a2+b2 )(a-b)
     (a+b)2x -  (a-b)(a+b)y = 4ab(a+b)          (adding)    
     ---------------------------------------------------------
2(a2+b2 ) x = 2a3 - 2a2b+2ab2 -2b3+4a2b+4ab2
2(a2+b2 ) x = 2a3 + 2a2b+6ab2 -2b3
x = 2(a3 + a2b+3ab2 -b3 ) / 2(a2+b2 ) 
 ∴ x = (a3 + a2b+3ab2 -b3 ) / (a2+b2 )  ,y = (a3 +b3 -a2b+3ab2 ) / (a2+b2 )
Hope this helps 
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