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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
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高一數學乘法公式
Oct 1st 2013, 14:10

得先知道 : (x+y)(y+z)(z+x)+xyz = (x+y+z)(xy+xz+yz)

然後開始做題目囉!

已知 x+y+z=(3+√7) / 2 , x^2+y^2+z^2 = (11+2√7) / 2

(x+y+z)^2 = x^2+y^2+z^2+2(xy+yz+xz) = 4+3√7/2

(x+y+z)^2 - x^2 - y^2 - z^2 = 2(xy+yz+xz) = (-3+√7)/2

得 : xy+yz+xz = (-3+√7)/4

故原式 : (x+y+z)(xy+xz+yz) = ((3+√7) / 2)((-3+√7)/4) = -1/4.....ans

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希望對您有幫助!

參考資料 mE

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