a²-ab-b²=0
(a-b/2)²-b²/4-b²=0
(a-b/2)²=5b²/4
a-b/2 = ±√5b/2
a = (1±√5)b/2
∵ a>0,b>0,即a,b同号,有a/b>0
∴ a=(1+√5)b/2