如果 **[ ] 入面既係次方** √ 係開方
X+X[-1]=√2 +1
咁:
x[2]+x[-2] = ?
Maths!! 10分
2007-12-28 2:27 am
回答 (3)
2007-12-28 2:45 am
✔ 最佳答案
由於 X+X[-1]=√2 +1 如果左右同時做平方, (由於觀察到 X * X[-1] = 1)
LHS = (X+X[-1])[2]
= X[2] + 2*X*X[-1] + X[-2]
= X[2] + X [-2] + 2
RHS = (√2 +1)[2]
= (√2)[2] + 2*√2*1 + 1[2]
= 2 + 2√2 + 1
= 3 + 2√2
由於LHS = RHS, 所以
X[2] + X [-2] + 2 = 3 + 2√2
所以 X[2] + X [-2] = 3 + 2√2 - 2 = 1 + 2√2
希望幫到你
參考: 自己既計算
2007-12-30 8:49 pm
x^2 + x^(-2)
= x^2 + 2 + x^(-2) - 2
= ( x + x^(-1))^2 - 2
we know that
x + x^(-1) = √2 + 1
sub
( x + x^(-1))^2 - 2
= ( √2 +1 )^2 - 2
= 2 + 2√2 + 1 - 2
= 2√2 + 1
= x^2 + 2 + x^(-2) - 2
= ( x + x^(-1))^2 - 2
we know that
x + x^(-1) = √2 + 1
sub
( x + x^(-1))^2 - 2
= ( √2 +1 )^2 - 2
= 2 + 2√2 + 1 - 2
= 2√2 + 1
參考: 自己
2007-12-28 2:44 am
x[2]+x[-2]
=2( X+X[-1])________________抽2出黎
=2(√2 +1 ) ________________ 因為X+X[-1]=√2 +1，所以sub入去
=2*√2 +2 or 4.8284(小數後4個位)
=2( X+X[-1])________________抽2出黎
=2(√2 +1 ) ________________ 因為X+X[-1]=√2 +1，所以sub入去
=2*√2 +2 or 4.8284(小數後4個位)
收錄日期: 2021-05-01 15:41:37
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https://hk.answers.yahoo.com/question/index?qid=20071227000051KK03548