Page 61 - Numbertheory

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12b ×15b ×16b = (3146)b :( )

(b + 2)(b + 5)(b + 6) = 3b 3 + b 2 + 4b + 6

b 3 +13b 2 + 52b + 60 = 3b 3 +b 2 + 4b + 6

2b 3 −12b 2 − 48b − 54 = 0

b 3 − 6b 2 − 24b − 27 = 0

(b − 9)(b 2 + 3b + 3) = 0

.b = 9 b 2 + 3b + 3 ≠ 0 b >1

sb = (b + 2) + (b + 5) + (b + 6) = 3b +13 = 3b + b + 4
= 4b + 4 = (44)b + (44)9

AMC12 AMC10 [AMC10A 2003] ( )

. AMC 10 + A MC 12 = 123422

12 ( ) 13 ( ) A + M +C

14 ( ) 15 ( )

:( )

AMC 10 + A MC 12 = 123422

AMC 00 + AMC 00 = 123400

. AMC = 1234 = 617 . AMC + A MC = 1234

2 CM A

.A =6 M =1 C =7

. A + M +C = 6 +1+ 7 =14

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