中學數學問題 第1題 求解

√(ab) / (√a＋√b)＝2
==> (√a＋√b) / √(ab)＝1/2
==> 1/√a + 1/√b = 1/2 ⋯⋯ (i)
Similarly,
√(bc) / (√b＋√c)＝3
==> 1/√b + 1/√c = 1/3 ⋯⋯ (ii)
√(ca) / (√c＋√a)＝5
==> 1/√c + 1/√a = 1/5 ⋯⋯ (iii)
(i) + (ii) + (iii) gives
1/√a + 1/√b + 1/√c = 31/60
So, 1/√a = 11/60, 1/√b = 19/60, 1/√c = 1/60
Therefore, √a = 60/11, √b = 60/19, √c = 60

So, a / √(bc)
= (60/11)(60/11) / [(60/19)(60)]
= 19/121