Given that A and B are the root of the equ. x^2-3x+p=0
if A^4+B^4 = 17 find the values of p
qua.equ. for a.maths
2008-07-14 3:44 pm
回答 (1)
2008-07-14 4:14 pm
✔ 最佳答案
sum of root:A+B=3
product of root:AB
=p
A4+B4 = 17
(A4+2A2B2+B4)-2A2B2=17
(A2+B2)2-2A2B2=17
[(A+B)2-2AB]2-2(AB)2=17
[(3)2-2(p)]2-2(p)2=17
(9-2p)2-2p2=17
(81-36p+4p2)-2p2=17
64-36p+2p2=0
(2p-4)(p-16)=0
∴p=16 or p=2//
收錄日期: 2021-04-23 20:33:29
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https://hk.answers.yahoo.com/question/index?qid=20080714000051KK00438