a/b

Algebra Level 1

If $a$ and $b$ are nonzero unequal real numbers and $\dfrac{a-b}{a} = \dfrac{b}{a-b}$ , what is the sum of all possible values for $\dfrac{a}{b}$ ?

1 solution

Danish Ahmed
Mar 20, 2015

Cross multiplying, we get $a^2-2ab+b^2=ab$ .

Simplifying, we have $a^2-3ab+b^2=0$

Dividing by $b^2$ , we get $\left(\dfrac{a}{b}\right)^2-3\cdot\left(\dfrac{a}{b}\right)+1=0$

Applying vietas, we get $\boxed{3}$