满足1/2∧a+1/2∧b=1,1/2∧(a+b)+1/2∧(a+c)+1/2∧(b+c)=1,则c的最大值
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ç±(1/2)^a +(1/2)^b=1å¾
(1/2)^a=1-(1/2)^b (1)
(1/2)^(a+b) +(1/2)^(a+c) +(1/2)^(b+c)=1
[(1/2)^a][(1/2)^b]+[(1/2)^a][(1/2)^c]+[(1/2)^b][(1/2)^c]=1
å¸¦å ¥ï¼1ï¼å¼å¾
[1-(1/2)^b][(1/2)^b]+[1-(1/2)^b][(1/2)^c]+[(1/2)^b][(1/2)^c]=1
[(1/2)^b]-[(1/2)^2b]+[(1/2)^c]-[(1/2)^b][(1/2)^c]+[(1/2)^b][(1/2)^c]=1
-[(1/2)^b]^2 +[(1/2)^b]+[(1/2)^c]-1=0
å¯ä»¥æä¸å¼çåå ³äºt=[1/2)^b]çä¸å äºæ¬¡æ¹ç¨ï¼
-t²+t+(1/2)^c -1=0
å该æ¹ç¨æå®æ°è§£ä¸è§£å¤§äº0ï¼
æä»¥å¿ é¡»ï¼â³=1²-4[(1/2)^c -1]â¥0
(1/2)^câ¤3/4
câ¤2-log2 (3)
æ cçæ大å¼æ¯2-log2 (3)
ç±(1/2)^a +(1/2)^b=1å¾
(1/2)^a=1-(1/2)^b (1)
(1/2)^(a+b) +(1/2)^(a+c) +(1/2)^(b+c)=1
[(1/2)^a][(1/2)^b]+[(1/2)^a][(1/2)^c]+[(1/2)^b][(1/2)^c]=1
å¸¦å ¥ï¼1ï¼å¼å¾
[1-(1/2)^b][(1/2)^b]+[1-(1/2)^b][(1/2)^c]+[(1/2)^b][(1/2)^c]=1
[(1/2)^b]-[(1/2)^2b]+[(1/2)^c]-[(1/2)^b][(1/2)^c]+[(1/2)^b][(1/2)^c]=1
-[(1/2)^b]^2 +[(1/2)^b]+[(1/2)^c]-1=0
å¯ä»¥æä¸å¼çåå ³äºt=[1/2)^b]çä¸å äºæ¬¡æ¹ç¨ï¼
-t²+t+(1/2)^c -1=0
å该æ¹ç¨æå®æ°è§£ä¸è§£å¤§äº0ï¼
æä»¥å¿ é¡»ï¼â³=1²-4[(1/2)^c -1]â¥0
(1/2)^câ¤3/4
câ¤2-log2 (3)
æ cçæ大å¼æ¯2-log2 (3)
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