Question

e urgentt, va rog mult de tott, sunt îngrijorat, va rog​

Answer 1

Explicație pas cu pas:

a)

$100a + 10b + c = 99a + 10b + (a + c) =$

$= 99a + 10b + b = 99a + 11b$

$= 11 \cdot (9a + b) \bf \ \ \vdots \ \ 11$

b)

$1000a + 100b + 10c + d = 1000a + 99b + 10c + (b + d) =$

$= 1000a + 99b + 10c + (a + c) = 1001a + 99b + 11c$

$= 11 \cdot (91a + 9b + c) \bf \ \ \vdots \ \ 11$

c)

$10000a + 1000b + 100c + 10d + e =$

$= 9999a + 1000b + 99c + 10d + (a + c + e)$

$= 9999a + 1000b + 99c + 10d + (b + d)$

$= 9999a + 1001b + 99c + 11d$

$= 11 \cdot (909a + 91b + 9c + d) \bf \ \ \vdots \ \ 11$

d)

$11 \ \Big| \ \overline {abc} \iff 11 \ \Big| \ (100a + 10b + c)$

$\iff 11 \ \Big| \ \Big(99a + a + 11b - b + c\Big)$

$\iff 11 \ \Big| \ \Big[11 \cdot \Big(9a + b\Big) + \Big(a - b + c\Big)\Big]$

$11 \ \Big| \ \Big[11 \cdot \Big(9a + b\Big)\Big] \implies \bf 11 \ \Big| \ \Big(a - b + c\Big)$

q.e.d.