Răspuns:
Explicație pas cu pas:
__ __ __
ab + bc + ca = 77
( 10a+b) + ( 10b+c) + (10c+a) = 77
(10a+a) + (10b+b)+(10c+c) = 77
11 a + 11 b + 11 c = 77
11 × ( a + b + c ) = 77
a + b + c = 77 : 11
a + b + c = 7; unde a, b, c ≠ 0
Solutii
(a, b, c) = (1, 1, 5); (1, 2, 4); ( 1, 3, 3); ( 1, 4, 2); ( 1, 5, 1); (2, 1, 4); (2, 4, 1);
( 2, 2, 3); ( 2, 3, 2); ( 3, 1, 3); (3, 2, 2); ( 3, 3, 1); ( 5, 1, 1)
( 2, 4, 1) ; ( 4, 2, 1)
_______________________
a = 1 si b = 1 => c = 7 - 1 - 1 = 5 → nu se precizeaza ca cifrele sa fie diferite
Numerele sunt:
__ __ __
ab + bc + ca
11 + 15 + 51 = 77 ( a = 1, b = 1 si c = 5)
15 + 51 + 11 = 77 ( a=1, b=5, c= 1)
51 + 11 + 15 = 77 ( a = 5,b = 1, c = 1)
12 + 24 + 41 = 77 ( a = 1 si b = 2 ⇒ c = 4 )
14 + 42 + 21 = 77 ( a = 1, b = 4 , c = 2 )
21 + 14 + 42 = 77 ( a = 2, b = 1, c = 4)
41 + 12 + 24 = 77 ( a = 4, b = 1, c = 2 )
13 + 33 + 31 = 77 (a = 1 si b = 3 ⇒ c = 3 )
31 + 13 + 33 = 77 ( a = 3, b = 1, c = 3 )
33 + 31 + 13 = 77 ( a = 3, b = 3, c = 1 )
22 + 23 + 32 = 77 ( a = 2, b = 2 si c = 3 )
23 + 32 + 22 = 77 ( a = 2, b = 3 si c = 2 )
32 + 22 + 23 = 77 ( a = 3, b = 2 si c = 2 )
24 + 41 + 12 = 77 ( a = 2, b =4 si c = 1 )
42 + 21 + 14 = 77 ( a = 4, b = 2 si c = 1)
