Question

初二黄金分割已知M,N是线段AB的两个黄金分割点,已知MN=20倍根号5-40,求AB长.

Answer 1

设AB = x

则AN = （√5 - 1）/2 * x

BM = （√5 - 1）/2 * x

所以MN = AN + BM - AB = （√5 - 1）/2 * x + （√5 - 1）/2 * x - x = 20√5 - 40

（√5 - 1）* x - x = 20√5 - 40

（√5 - 2）x = 20√5 - 40

x = 20

所以AB = 20