Question

aflati toate perechile de cifre (a,b) stiind ca a,b+b,a=12,1
cât de repede posibil​

Answer 1

Răspuns:

Explicație pas cu pas:

a,b = a + 0,1b

b,a = b = 0,1a

a,b + b.a = 12,1

a + 0,1b + b + 0,1a = 12.1

1,1a + 1,1b = 12,1

a + b = 12,1 : 1,1 = 11

11 = 2 + 9 = 3 + 8 = 4 + 7 = 5 + 6

(1,9); (3,8); (4,7); (5,6); (9,1); (8,3); (7,4); (6,5)

Answer 2

$\it \overline{a,b}+\overline{b.a}=12,1|_{\cdot10} \Rightarrow \overline{ab}+\overline{ba}=121 \Rightarrow 10a+b+10b+a=121 \Rightarrow \\ \\ \Rightarrow 11a+11b=121 \Rightarrow 11(a+b)=121|_{:11} \Rightarrow\\ \\ \Rightarrow a+b=11=2+9=3+8=4+7=5+6=6+5=7+4=8+3=9+2\\ \\ (a,\ b)\in\{(2,\ 9),\ (3,\ 8),\ (4,\ 7),\ (5,\ 6),\ (6,\ 5),\ (7,\ 4)\ (8,\ 3),\ (9,\ 2) \}$