呢條係96年a-maths會考其中一條題目既某部份
已知 h = √5 , (alpha, beta 用a 同 b黎代表) a+b = h ,ab = 1
點解呢, a(alpha) or b(beta)會 = (√5±1)/2 ????
有一條f4 a-maths唔明...
2007-10-01 11:41 pm
回答 (1)
2007-10-02 12:55 am
✔ 最佳答案
a+b = h = √5, so a = √5 -b --------------(1)ab = 1 ------------------------(2)
put (1) into (2)
( √5 -b ).b = 1
b^2 - √5b +1 = 0
b = ( √5 +/- √(5-4) ) / 2
b = (√5±1)/2
if b (√5+1)/2, then a = √5 - (√5+1)/2 = (√5-1)/2
if b (√5-1)/2, then a = √5 - (√5-1)/2 = (√5+1)/2
so a,b = (√5±1)/2
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