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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
---------------------希望對您有幫助!
參考資料 mE
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