(A2/X+B2/Y) * (X+Y) = A2+A2Y/X+B2X/Y+B2 ≥ A2+B2+2 radical (a 2y/x) * (b 2x
= a 2+b 2+2ab = (a+b) 2 so a 2/x+b 2/y ≥ (a+b) 2/(x+y)
The equal sign condition is (a 2y/x) = (b 2x/y), that is, y/x = b/a.