Question

rezolvati ecuatia: 0,(1x) ( cu bara deasupra) + 0,(2x) ( cu bara deasupar)+...+0,(9x ) (cu bara deasupara)=x

Answer 1

Vom scrie ca toate elementele ca fractie ordinara.
1x, 2x, ..., 9x - vor fi cu bara deasupra

1x / 99 + 2x / 99 + ... + 9x / 99 = x
(1x + 2x + ... + 9x) / 99 = x
Descompunem in baza zece numerele 1x, 2x, ..., 9x:

((10 + x) + (20 + x) + ... + 90 + x) / 99 = x
(10 + 20 + ... + 90 + 9x) / 99 = x
(10(1 + 2 + ... + 9) + 9x) / 99 = x
(10 * 45 + 9x) / 99 = x
(450 + 9x) / 99 = x
(50 + x) / 11 = x
50 + x = 11x
10x = 50
x = 5