If x + y = a & xy = b, express the following in terms of a & b.
1.x的4次方 + y的4次方-------x4+y4
2.(x-y)的2次方--------(x-y)2
3.x的3次方 + y的3次方----------x3+y3
MATHS!!!QUICK~~~
2008-06-26 6:14 pm
回答 (2)
2008-06-26 7:14 pm
✔ 最佳答案
(x的4次方=x^4)1.
since (x+y)^4=x^4+4x^3y+6x^2y^2+4xy^3+y^4
x^4+y^4=(x+y)^4-4xy(x^2+y^2)-6(xy)^2
=a^4-4b{(x+y)^2-2xy}-6b^2
=a^4-4b{a^2-2b}-6b^2
2.
(x-y)^2=x^2-2xy+y^2
=(x+y)^2-4xy
=a^2-4b
3.
since (x+y)^3=x^3+3x^2y+3xy^2+y^3
x^3+y^3=(x+y)^3-3xy(x+y)
=a^3-3ab
2008-06-26 11:16:14 補充：
手寫返一次就睇得明gala
2008-06-27 10:28:00 補充：
下面唔該唔好抄答案
仲要連抄緊乜都唔知
參考: 自己
2008-06-26 10:08 pm
(x+y)^4=x^4+4x^3y+6x^2y^2+4xy^3+y^4
=a^4-4b(a^2-2b)-6b^2
(x-y)^2=x^2-2xy+y^2
=(x+y)^2-4xy
(x+y)^3=x^3+3x^2y+3xy^2+y^3
=a^3-3ab
=a^4-4b(a^2-2b)-6b^2
(x-y)^2=x^2-2xy+y^2
=(x+y)^2-4xy
(x+y)^3=x^3+3x^2y+3xy^2+y^3
=a^3-3ab
參考: myself
收錄日期: 2021-04-21 14:47:31
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https://hk.answers.yahoo.com/question/index?qid=20080626000051KK00577