Re: [中學] 一題中學數學問題

看板Math作者LiamIssac (Madchester是這群人壓根)時間7年前 (2018/02/26 18:29)推噓3(3推 0噓 1→)

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※ 引述《skyfan2008 (la..la..)》之銘言： : 若x,y皆是正整數，滿足x^2=y^2(x+y^4+2y^2)的數對(x,y)=? : 請教各位大大如何解 : 謝謝亂猜的各為高手看一下對不對 let t == y^2 then we have x^2 - t*x - (t^3 + 2t^2) = 0 So the positive root of this equation in terms of x is x = 0.5*(t + \sqrt{4t^3 + 9t^2}) But since x is in N, so t must be some 2*a for which a = 1,2,3,4... so that the 0.5 can be balanced off Then we plug in t = 2*a in the sqrt term, which must be some squared number it follows that 4t^3 +9t^2 = a^2(32a + 36) for a = 1, 2, 3, 4... and we need only care about 32a + 36 being some squared number ... then we go over all possible a's to get the answer the smallest answer is a = 2 -> t = 4 (y = 2) -> x = 12 -- 有錯請指正^^" -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 163.18.23.206 ※ 文章網址: https://www.ptt.cc/bbs/Math/M.1519640983.A.904.html ※ 編輯: LiamIssac (163.18.23.206), 02/26/2018 18:29:59 ※ 編輯: LiamIssac (163.18.23.206), 02/26/2018 18:30:22

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Starvilo

02/26 19:08, 7年前 , 1^F

02/26 19:08, 1^F