推 xz35s8pq : 感謝 09/15 12:17
→ yyc2008 : 有沒有解題思路? 看不懂為何會想這麼做 09/16 00:07
→ suker : 算硬湊(x-1) 能否開出漂亮(1/3)次方.. 09/16 10:50
推 gwendless : 思路大概就是 1.設定適當未知數 2.三次方公式湊合 09/17 02:14
→ gwendless : 是一個比較需要靈感的題目。 09/17 02:14
※ 引述《xz35s8pq ()》之銘言：
: https://i.imgur.com/QKkt0DA.jpg
: 試過配方 拆開比較係數 或是移項再立方但還是解不出來，希望各位大師能幫忙解惑！
有夠難打的 提供參考
令x=2^(1/3) ==>x^3 =2
令原式y=(x-1) ^ (1/3)
(x+1)^3 = x^3+ 3x^2 +3x +1 = 3(x^2+x+1)
^^^^
=2
左右2邊 *(x-1)
(x-1) (x+1)^3 = (x-1) 3(x^2+x+1) = 3 (x^3 -1) = 3
^^^
=2
3
(x-1) = --------------
(x+1)^3
左右開3次方
3^(1/3)
(x-1) ^(1/3) = y = ---------------
x+1
3^(1/3) (x^2-x+1)
y = ------------ * ---------------
(x+1) (x^2-x+1)
x=2^(1/3) 代入
3^(1/3) *{4^(1/3) -2^(1/3)+1}
= ------------------------------------
x^3 +1
^^
=2
3^(1/3) *{4^(1/3) -2^(1/3)+1}
= --------------------------------- {把 3^(1/3) 除到分母}
3
{4^(1/3) -2^(1/3)+1}
= ----------------------------- = (4/9)^(1/3) -(2/9)^(1/3)+(1/9)^(1/3)
9^(1/3)
a+b+c= 4/9 -2/9 +1/9 =1/3
--
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※ 編輯: suker (111.251.196.151 臺灣), 09/15/2019 09:02:30