F2 奧數 plz

Since x > 0, then x+ 1/x > = 2, then
b= 2a^2/(1+a^2)= 2a/(a+ 1/a) < = a
similarily, c=2b^2/(1+b^2) < = b, a=2c^2/(1+c^2) < = c
so b < = a < = c < = b, then a=b=c

2a^2/(1+a^2) = b= a, then a=1

the area of triangle ABC = sqrt(3) /4

可唔可以話看到 a=b=c?

Can Heron's formula do something here.

2013-10-13 02:33:36 補充：
Sorry, 對 奧數 無甚認識，咁唔怪得要等啦！

what is 彩虹?

都係等彩虹啦～～～～

2013-10-13 01:34:43 補充：
但係中二應該未學 Heron's formula......

2013-10-13 02:39:07 補充：
大家咁話，我個人就等彩虹出現，但可能亦都有其他可以解答的會員～

^__^

2013-10-14 15:39:23 補充：
cas，呢個部份我則有能力幫幫你 (=^o^=)

For x > 0, √x is real.

(√x - 1/√x )² ≥ 0

x - 2√x (1/√x) + 1/x ≥ 0

x - 2 + 1/x ≥ 0

x + 1/x ≥ 2