If a,b >0 and b/a satisfies the proportion b/a=(a+b)/b, then $\frac{b}{a}\equiv r=\frac{1+\sqrt{5}}{2}$.
If c,d >0 and c/d satisfies the proportion d/c=c/(c+d), then $\frac{d}{c}\equiv r=\frac{\sqrt{5}-1}{2}$.
2. In the first one, let $t = \frac{b}{a}$. Solve the quadratic with t.