已知成等差數列的三個正數和為15, 並且言三個數分別加上1,3,9就成等比數,求這三個數
設最小的數為x，差為n
x+x+x+3n = 15
x+n = 5 (1) ←我明白
我唔明白下列步驟：
x+n+3 x+2n+9 ← 我唔明白點嚟
_______ = _______
x+1 x+n+3
代入(1),
64 = (14+n)(x+1)
x = 3
n = 2 <----正確
數列唔明白,請解釋
2008-03-17 6:57 am
回答 (2)
2008-03-17 7:49 am
✔ 最佳答案
三個數 x - d, x, x + dx - d + x + x + d = 15
x = 5
三個數 5 - d, 5, 5 + d
加上1, 3, 9
三個數 6 - d, 8, 14 + d
8/(6 - d) = (14 + d)/8
(14 + d)(6 - d) = 64
d^2 + 8d - 20 = 0
(d - 2)(d + 10) = 0
d = 2 or d = -10 (rejected, 三個數要正數)
三個數 2, 5, 7
咁做係咪易 d,
2008-03-18 6:33 pm
等差數列的三個正數和為15
let the smallest value be x，the value between two # be a.
x+(x+a)+(x+2a)=15
x+a=5 (1)
(x+a+3)^2=(x+1)(x+2a+9)
(5+3)^2=(x+1)(5+9+a)
8^2=(x+1)(14+a)
x=5-a
64=(5-a+1)(14+a)
64=(6-a)(14+a)
64=84-8a^2
a^2-8a+20=0
a=2,-10
x=5-a
x=3
let the smallest value be x，the value between two # be a.
x+(x+a)+(x+2a)=15
x+a=5 (1)
(x+a+3)^2=(x+1)(x+2a+9)
(5+3)^2=(x+1)(5+9+a)
8^2=(x+1)(14+a)
x=5-a
64=(5-a+1)(14+a)
64=(6-a)(14+a)
64=84-8a^2
a^2-8a+20=0
a=2,-10
x=5-a
x=3
參考: myself
收錄日期: 2021-05-03 16:15:11
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