Re: [中學] 甄選題
※ 引述《ristvakbean (有夠優秀)》之銘言：
: (4)利用根與係數,若a,b,c是異於零的互異實數,且a^3x+a^2y+az=1,b^3x+b^2y+bz=1
: ,c^3x+c^2y+cz=1,則x=?,y=?,z=?
|a^3 a^2 a| [x] [1]
|b^3 b^2 b| [y] = [1]
|c^3 c^2 c| [z] [1]
Δ = abc(a-b)(a-c)(b-c)
Δx= (a-b)(a-c)(b-c)
Δy= (a-b)(a-c)(c-b)(a+b+c)
Δz= (a-b)(a-c)(b-c)(ab+bc+ca)
hence, x=1/(abc)
y=-(a+b+c)/(abc)
z=(ab+bc+ca)/(abc)
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