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發表 gkw0824usa 於 星期四 一月 18, 2007 11:00 pm

#ed_op#DIV#ed_cl#Ahh~ I see, thanks! I didn't even realize that!#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#No wonder I felt skeptical about my solution to the problem.#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#It shouldn't be that complicated!#ed_op#IMG src="/phpBB2/richedit/smileys/8.gif"#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

發表 skywalker 於 星期四 一月 18, 2007 8:08 pm

#ed_op#DIV#ed_cl#易知四根合為0,其中兩根合為2,則另兩根之合為-2#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#令四根為#ed_op#FONT size=4#ed_cl#α, β, γ, δ,且α+β=-2,γ+δ=2#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl##ed_op#/FONT#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl#原方程式=(x^+2x+αβ)(x^2-2x+γδ)=0....(1)#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl##ed_op#/FONT#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl#再令αβ=a,γδ=b#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl##ed_op#/FONT#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl#(1)=>(x^+2x+a)(x^2-2x+b)=0#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl##ed_op#/FONT#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl#比較係數得#ed_op#/FONT#ed_cl##ed_op#FONT size=4#ed_cl#a-b=4,#ed_op#/FONT#ed_cl##ed_op#FONT size=4#ed_cl#a+b=-6#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl##ed_op#/FONT#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl#a=-1,b=-5#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl##ed_op#/FONT#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl#k=5,(1)=(x^2-2x-1)(x^2+2x-5)#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl##ed_op#/FONT#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=4#ed_cl#=>x=-1+-√6或1+-√2#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl#

發表 gkw0824usa 於 星期三 一月 17, 2007 1:26 pm

skywalker 寫到:#ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#其實不需要用到那麼麻煩#ed_op#/DIV#ed_cl#
#ed_op#DIV#ed_cl#請指教#ed_op#IMG src="/phpBB2/richedit/smileys/yy04.gif"#ed_cl##ed_op#/DIV#ed_cl#

發表 skywalker 於 星期二 一月 16, 2007 9:54 pm

#ed_op#DIV#ed_cl#答案有誤喔#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#其實不需要用到那麼麻煩#ed_op#/DIV#ed_cl#

發表 gkw0824usa 於 星期二 一月 16, 2007 2:01 pm

#ed_op#DIV#ed_cl#By Vieta's formula, we know that there must exist a factor that is x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-2x+a,#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#therefore we can let the factors of the initial equation be#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#                      x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-2x+a#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#            x )      x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+bx+c #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#         #ed_op#STRIKE#ed_cl#                                  #ed_op#/STRIKE#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#1. We know that the coefficient of x#ed_op#SUP#ed_cl#3#ed_op#/SUP#ed_cl# is 0,#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#    therefore, b-2=0 → b=2.#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#2. We know that the coefficient of x#ed_op#SUP#ed_cl#2 #ed_op#/SUP#ed_cl#is -10,#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#    hence, a+c-2b=-10 → a+c=-6#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#3. We know that the coefficient of x is 8,#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#    thus -2c+ab=8 → a-c=4#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#4. By a+c=4, a-c=4 we know a=-1, c=-5#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#    therefore, k=ac=5#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#5. By those above, we could find out:#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#initial equation#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#→(x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-2x-1)(x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+2x-5)=0#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#IMG alt="image file name: 2k957475bdb4.gif" src="http://yll.loxa.edu.tw/phpBB2/richedit/upload/2k957475bdb4.gif" border=0#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#Thanks, I've corrected it#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

[數學]代數題..

發表 skywalker 於 星期一 一月 15, 2007 10:19 pm

#ed_op#DIV#ed_cl#已知x^4-10x^2+8x+k=0有兩根的合為2,試求常數k與其四根#ed_op#/DIV#ed_cl#