Question

ab+by=2ab/a²+b²
bn+ay=1
Then (x²+y²)(a²+b²)=?

Answer 1

Given ax + by = 1 , bx+ay = [(a+b)2 ]/ [a2 +b2] - 1 ax + by = 1  ----------------(1) , bx+ay = 2ab/ [a2 +b2]  --------------(2) adding (1) and (2) (a+b)x + (a+b)y = 1 + 2ab/ [a2+b2]  (a+b)(x + y)  = (a+b)2 / [a2 +b2]  x + y = (a+b) / [a2 +b2]   ---------------(3)substracting (2) from (1) (a-b)x - (a-b)y = 1 - 2ab/ [a2 +b2]  (a-b)(x - y)  = (a-b)2 / [a2+b2]  x - y = (a-b) / [a2 +b2]   ---------------(4)adding (3) and (4) 2x = 2a / (a2 +b2) x  = a / (a2 +b2) . substracting (4) from (3) 2y = 2b / (a2 +b2 )  y = b / (a2 +b2 ) Therefore the solution x  = a / (a2 +b2)   y = b / (a2+b2 )