Question

Determina numărul natural zi pentru care 7×x+14×x+21×x+.......+126×x=7×9×18

Answer 1

7x+14x+...............+126x=7*9*18
7(x+2x+3x+.......+18x)=7*9*18  impartim totul prin 7
x+2x+3x+.......+18x=9*18    
in partea stanga avem suma lui Gauss de la 1 la 18
18(1+18)/2=18*19/2=19*9

avem
19*9x=9*18
19x=18
x=18/19

Answer 2

7x+14x+21x+.......+126x=7·9·18
7x(1+2+..+18)=7·9·18
7x·18·19:2=7·9·18 / : 7·9
2x·19:2=18
19x=18
x=18/19