Re: [中學] 高一 小數轉分數

[mack (腦海裡依然記得妳)]

※ 引述《baby7676 (北鼻漆掉漆掉)》之銘言：
: 這題想了一下 不知怎下手~麻煩各位指點迷津
:   設x,y,z為1到9的正整數，若x,y,z成等差數列，
:       _   __   __
:   且0.x+0.4y=1.2z ，則x+y+z=?
:      (循環節的意思)
x,y,z成等差數列 => 2y = x + z => z = 2y - x
  __   __   __
0.xx+0.4y=1.2z => (10x+x) + (40+y) = (120+z-1)
               => (10x+x) + (40+y) = (120+2y-x-1)
               => 11x + y + 40 = 2y - x + 119
               => 12x = y + 79 ≦ 9 + 79 = 88
               => x ≦ 88/12 = 7. ...
=> x = 7 => y = 5 => z = 3
=> x + y + z = 15

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 111.252.229.77
→ baby7676    :感謝喔~~!!