If a and b are nonzero unequal real numbers and (a−b)/a = b/(a−b), what is the sum of all possible
values for a/b?
I had no idea where to start with this one.
(a−b)a=b(a−b)(a−b)2=aba2−2ab+b2=aba2−3ab+b2=0a2+(−3b)a+(b2)=0a=3b±√9b2−4b22a=3b±b√52
a=3b±b√52ab=3±√52if you add those two possibilities the sum is 6/2=3
You neeed to check this carefully.