數學知識交流-分情況討論2題

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2011-02-22 23:05:23 補充：
(1) 更正,
2>=(b-1)(c-1)若其中一數=1,另一數可以是任何數,否則b,c不能大於3
設b=1,則a+1+c=ac=>ac-a-c-1=0
ac-a-c+1=2
(a-1)(c-1)=2
則其中一數是2,另一數是3

2011-02-26 23:31:00 補充：
Reload the image:
http://i1090.photobucket.com/albums/i376/Nelson_Yu/14.jpg

1)
不妨 a ≥ b ≥ c , 則

a+b+c

= abc ≤ 3a

bc ≤ 3

當 bc = 3 ,
b = 3 , c = 1,
a + 3 + 1 = a*3*1
a = 2 (不合)

當 bc = 2 ,
b = 2 , c = 1,
a + 2 + 1 = a*2*1
a = 3

當 bc = 1 ,
b = 1 , c = 1,
a + 1 + 1 = a*1*1 (無解)

2011-02-22 23:26:14 補充：
0 也是自然數,所以 a = b = c = 0