※ 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 ?
(1)
b a 17
----- + ----- = ----
a+c b+c 20
b(b+c) + a(a+c) 17
=> ------------------ = ----
(a+c)(b+c) 20
b^2 + bc + a^2 + ac 17
=> ----------------------- = ----
ab + ac + bc + c^2 20
c^2 + ac + bc 17
=> ------------------------ = ----
ab + ac + bc + c^2 20
ab + c(a+b+c) 20
=> ----------------- = ----
c(a+b+c) 17
17
=> c(a+b+c) = ---- ab
3
(2)
b(c-a) a(c-b) 17
原式 => ----------- + ----------- = ----
c^2 - a^2 c^2 - b^2 20
c-a c-b 17
=> ----- + ----- = ----
b a 20
a(c-a) + b(c-b) 17
=> ----------------- = ----
ab 20
ac - a^2 + bc - b^2 17
=> --------------------- = ----
ab 20
17 17
=> ac + bc - c^2 = ---- ab => c(a+b-c) = ----ab
20 20
(1) a+b+c 20 17
----- => -------- = ---- => c = ---- (a+b)
(2) a+b-c 3 23
代入 c^2 = a^2 + b^2 => 120 a^2 - 289 ab + 120 b^2 = 0
=> (8a - 15b)(15a - 8b) = 0 => a:b = 15:8 或 8:15
故 a:b:c = 15:8:17 或 8:15:17
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