数学高手进！紧急问题
答案:5 悬赏:0 手机版
解决时间 2021-05-17 00:48
- 提问者网友：wodetian
- 2021-05-16 11:40
已知a+b=p,ab=q,求a^5+b^5值
最佳答案
- 五星知识达人网友：鸠书
- 2021-05-16 12:26
a^2+b^2=(a+b)-2ab=p^2-2q
a^3+b^3=(a+b)(a^2-ab+b^2)=p(p^2-2q-q)=p^3-3pq
a^5+b^5=(a^2+b^2)(a^3+b^3)-a^2b^2(a+b)
=(p^2-2q)(p^3-3pq)-pq^2
=p^5-5p^3q+6pq^2-pq^2
=p^5-5p^3q+5pq^2
1
a^3+b^3=(a+b)(a^2-ab+b^2)=p(p^2-2q-q)=p^3-3pq
a^5+b^5=(a^2+b^2)(a^3+b^3)-a^2b^2(a+b)
=(p^2-2q)(p^3-3pq)-pq^2
=p^5-5p^3q+6pq^2-pq^2
=p^5-5p^3q+5pq^2
1
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全部回答
- 1楼网友：人類模型
- 2021-05-16 16:35
题目呢？
- 2楼网友：野味小生
- 2021-05-16 16:01
(a+b)^5=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5=a^5+b^5+5ab(a^3+b^3)+10a^2b^2(a+b)
=a^5+b^5+5q(a+b)(a^2-ab+b^2)+10q^2p=a^5+b^5+5pq(p^2-3q)+10q^2p
a^5+b^5=p^5-5p^3q+15pq^2-10q^2p
a^5+b^5=p^5-5p^3q+5pq^2
- 3楼网友：过活
- 2021-05-16 14:37
(a+b)^5=a^5+b^5+5aaaab+10aaabb+10aabbb+5abbbb=p^5
则a^5+b^5=p^5-10(a+b)qq-5(aaa+bbb)q=p^5-10pqq-5(a+b)(aa-ab+bb)q=p^5-10pqq-5p(pp-3q)q=p^5+5pqq-5pppq
- 4楼网友：骨子里都是戏
- 2021-05-16 13:26
a^5+b^5=a^5+b^5+2(ab)^3-2(ab)^3=(a^3+b^3)^2-2(ab)^3=[(a+b)(a^2-ab+b^2)]-2(ab)^3=[(a+b)((a+b)^2-3ab]-2(ab)^3=[p(p^2-3q)]-2q^3
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