已知P点是线段AB的黄金分割点,较短线段PB长为(6-2√5)厘米,则线段AB=____

问题描述:

已知P点是线段AB的黄金分割点,较短线段PB长为(6-2√5)厘米,则线段AB=____

黄金分割比 = (√5-1)/2 ≈ 0.618
已知P点是线段AB的黄金分割点,较短线段PB长为(6-2√5)厘米,则线段AB=____
AB = 6-2√5 x 2 ÷ [2-(√5-1) ]
= 2(6-2√5 ) ÷ (3-√5)
= 2 (6-2√5) (3+√5) /( 9-5)
= 2 (3-√5) (3+√5) / 2
= 9- 5
=4