Factorize(x二次+y二次)

👨🏻‍🏫 學術台數學

Kenneth

2009-09-26 3:45 am

Factorize
(x二次+y二次)

更新1:

emilylou1121, william441999, pc7086 喂，係(x^2-y^2)=(x+y)(x-y)

更新2:

william441999, sorry you are right!

回答 (6)

用戶108605

2009-11-02 3:43 am

Let z be -y^2.
x^2+y^2
=x^2-(-y^2)
=x^2-z^2
=(x+z)(x-z)
=[x+開方-y^2][x+開方-y^2]
Since 開方(ab)=開方a x 開方b
Therefore 開方-y^2=開方-1 x 開方y^2=y開方-1
Therefore [x+開方-y^2][x+開方-y^2]=(x+y開方-1)(x-y開方-1)
開方負1在數學上稱i
所以x^2+y^2=(x+yi)(x-yi)

2009-11-01 19:43:48 補充：
http://zh.wikipedia.org/zh-tw/%E8%99%9A%E6%95%B0
這是關於i的更多資料
不過i 在中學課程中也是較後的課題
在未打好factorize的觸覺基礎時就不要進一步思考這條問題

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用戶2053

2009-09-29 8:07 am

005 doraemonlam1994 的答案『 (x+y)^2-2xy』不算 Factorize,
Factorize 的答案必須是乘式 , 而『 (x+y)^2-2xy』只是減式。

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[匿名]

2009-09-27 2:56 am

2樓同4樓你地記錯啦
(x^2+y^2)(x^2-y^2)係=x^2-y^2
x^2+y^2
=(x^2+2xy+y^2)-2xy
=(x+y)^2-2xy

參考: 我

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[匿名]

2009-09-26 4:58 am

By Using Identities (a^2+b^2) = (a+b)(a-b)
So (x^2+y^2)
=(x+y)(x-y)

Prove That (x+y)(x-y) = (x^2+y^2)
(x+y)(x-y)
=x(x-y)+y(x-y)
=x^2-xy+xy+y^2
=(x^2+y^2)

2009-09-26 20:44:39 補充：
thx doraemonlam1994,,we are really wrong!!

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sheung

2009-09-26 4:05 am

(x^2+y^2-y^2-y^2+y^2+y^2)
=(x+y)(x-y)+(y^2)+(y^2)
x(x-y)+y(x-y)+y(y)+y(y)
x(x-y)+y(x+y)

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用戶207963

2009-09-26 4:02 am

(x² + y²) 等於 (x+y)乘(x-y)

參考: 我

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收錄日期: 2021-04-21 22:02:40
原文連結 [永久失效]:
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