Question

determinati numerele naturale de doua cifre ab stiind ca suma dintre numar si rasturnatul sau este 77

Answer 1

ab = numarul

ba = rasturnatul sau

ab + ba = 77

10 × a + b + 10 × b + a = 77

11 × a + 11 × b = 77

11 × ( a + b ) = 77

a + b = 77 : 11

a + b = 7

a si b diferite de 0

ab = 16; 25; 34; 43; 52; 61 .
_____________________

16 + 61 = 77

25 + 52 = 77

34 + 43 = 77

52 + 25 = 77

61 + 16 = 77

Answer 2

$\it \overline{ab}+\overline{ba} = 77 \Rightarrow 10a+b+10b+a=77 \Rightarrow 11a+11b=77 \Rightarrow \\ \\ \Rightarrow 11(a+b) = 77|_{:11} \Rightarrow a+b=7 \Rightarrow \overline{ab} \in\{16,\ 25,\ 34,\ 43,\ 52,\ 61\}$