👤

arata ca ab+bc+cd+da=ad+dc+cb+ba, unde a, b, c, d sunt cifre nenule

Răspuns :

ab + bc + cd + da = ad + dc + cb + ba

10 a + b + 10 b + c + 10 c + d + 10 d + a = 10 a + d + 10 d + c + 10 c + b + 10 b + a

11 a + 11 b + 11 c + 11 d   = 11 a + 11 b + 11 c + 11 d

11 ( a + b + c + d ) = 11 ( a + b + c + d )   l   : 11

a + b + c + d = a + b + c + d;   a, b, c, d ≠ 0