Re: [中學]數與數線
※ 引述《adamchi (adamchi)》之銘言：
: 1.a,b,c為任一三角形的邊長,證明abc >= (b+c-a)(c+a-b)(a+b-c)
Set A = b+c-a, B = c+a-b, C = a+b-c
It's equivalent to prove :
( (B + C)/2 )( (C + A)/2 )( (A + B)/2 ) ≧ABC
Which is obviously hold by AM-GM inequality.
: 2.x>3,當x=___,使得(x+6)/(x-3)^1/2 有最小值,且最小值為____
By AM-GM inequality :
(x+6)/(x-3)^1/2 = (x-3+9)/(x-3)^1/2 = √(x-3) + 9/√(x-3) ≧2*√9 = 6
The inequality attains it's minimum 6 at x = 12.
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