Re: [中學] 一題數學
※ 引述《ckchi (飄)》之銘言：
如果你對於題目有任何問題可以告知主辦的單位
17758這篇也是問雙週一題第一題
每一題都有問題嗎?
這樣再去投稿有意義嗎?
我想還是維持公平性會比較好~
相信斗六高中的學生應該是有能力自己解出來的
或者可由我幫你轉告你數學老師給你一些指導?
有沒有拿到獎是其次, 重點是這過程你學到什麼
我想這才是最重要的!
: → qoolinboy :有沒有全部是相異實數的解 03/12 19:05
: 來回答這個問題
: a式: x + y + z = w
: b式: 1/x + 1/y + 1/z = 1/w
: a代入b: 1/x + 1/y + 1/z = 1/(x+y+z)
: (xy+yz+yz)/xyz = 1/(x+y+z)
: 由於 x,y,z,x+y+z都不為0
: 所以：
: (x+y+z)(xy+yz+zx) = xyz
: => (x+y+z)(xy+yz) + (x+y+z)*xz = xyz
: => y(x+y+z)(x+z) + xz(x+z) = 0
: => (x+z)[y(x+y+z)+xz] = 0
: => (x+z)[y^2+(x+z)y+xz] = 0
: => (x+z)(y+x)(y+z) = 0
: 換言之， x =-z or x =-y or y =-z
: 即： w = y or w = z or w = x
: 所以沒有4個數都相異的解
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