Question

如图,已知AB=a,点D、C在线段AB上,且AC²=AB×BC,BD²=AD×AB,求DC的长.

Answer 1

∵AC²=AB×BC

∴AC²=a(a-AC)

AC²+a·AC-a²=0

∴AC=(-1±√5)/2·a

∵AC>0

∴AC=(-1+√5)/2·a

同理BD=（-1+√5）/2·a

∴AD=AB-BD=a-(-1+√5)/2·a=(3-√5)/2·a

∴CD=AC-AD=(-1+√5)/2·a-(3-√5)/2·a=(√5-2)/2·a