※ 引述《harry921129 (哈利~~)》之銘言：
: c^2 = a^2 + b^2
: 且
: b a
: --- + ----= 17/20
: a+c b+c
: 求 a:b:c ?
a b
令--- = x , --- = y
c c
則 x^2 + y^2 = 1
且
1 1 17
---------- + ------------ = ----
x 1 y 1 20
--- + --- --- + ---
y y x x
==>
y x 17
------- + ------- = ----
x + 1 y + 1 20
==>
x + y + 1 17
---------------- = ----
(x + 1)(y + 1) 20
17xy +17(x+y) + 17 = 20(x+y) + 20
17xy - 3(x+y) - 3 = 0
34xy - 6(x+y) - 6 = 0
17[(x+y)^2 - (x^2 + y^2)] - 6(x+y) - 6 = 0
令 A = x+y
17(A^2 - 1) - 6A - 6 = 0
17A^2 - 6A - 23 = 0
(17A - 23)(A + 1) = 0
A = x+y = 23/17 or -1(不合)
7
(x-y)^2 = 2(x^2 + y^2) - (x+y)^2 = 2 - (x+y)^2 = (--)^2
17
==>
x - y = ±7/17
I II
x + y 23/17 23/17
x - y 7/17 -7/17
x 15/17 8/17
y 8/17 15/17
a:b:c I. 15/17 : 8/17 : 1 = 15 : 8 : 17
II. 8/17 : 15/17 : 1 = 8 : 15 : 17
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※ 編輯: Tiderus (123.240.102.135), 01/18/2017 23:31:11