※ 引述《imaft ()》之銘言：
: 1.︱1-1/4-1/11-1/1998︱+︱1-1/4+1/11-1/1998︱=?
1 1 1
1 - --- - ----- - ------ > 0
4 11 1998
1 1 1
1 - --- + ----- - ------ > 0
4 11 1998
故得
1 1
(1 - --- - ------ ) * 2
4 1998
2995
= ------
1998
: 2. a+b+c=0 ︱︱a︱/(b+c) + ︱b︱/(c+a) + ︱c︱/(a+b) ︱ = x
: (x^200) - 4x + 2009 = ? (a,b,c為有理數，均不為0)
: 想了很久，還是沒解出來，希望有過程及答案，謝謝
| |a| |b| |c| |
| ----- + ----- + ----- | = x
| (b+c) (c+a) (a+b) |
| |a| |b| |c| |
=>| ----- + ----- + ----- | = x
| -a -b -c |
=> 1 = x
因為 a+b+c=0 , a,b,c 不為0
所以 a,b,c 為 1正2負 或 2正1負
|a|
當 a > 0, 則 ----- = -1
-a
|a|
當 a < 0, 則 ----- = 1
-a
故
當1正2負
x = | -1 | = 1
當2負1正
x = | 1 | = 1
得
100
x - 4x + 2009
= 1 - 4 + 2009
= 2006
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