Question

rezolvati exercițiul din imagine!va rog repedee​

Answer 1

(11x-1)/990+(22x-2)/990+(33x-3)/990+....+(99x-9)/990=4923/990

11x-1+22x-2+33x-3+....+99x-9=4923

11x+22x+33x+...+99x=4923+1+2+3+..+9

11x+22x+33x+...+99x=4923+45

11x+22x+33x+...+99x=4968

100+10+x+200+20+x+300+30+x+...+900+90+x=4968

4500+450+9x=4968

9x=18

x=2

Answer 2

Răspuns:

Explicație pas cu pas:

0,1(1x) = (11x - 1)/990 = 11x/990 - 1/990

0,2(2x) = (22x - 2)/990 = 22x/990 - 2/990

0,3(3x) = (33x - 3)/990 = 33x/990 - 3/990

.............

0,9(9x) = (99x - 9)/990 = 99x/990 - 9/990

_______________

S = 11x/990 + 22x/990 + 33x/990 + ...+ 99x/990 - (1/990 + 2/990 + 3/990 + ...+ 9/990)

1/990 + 2/990 + 3/990 + ....+ 9/990 = (1 + 2 + 3 + ...+ 9)/990 = 45/990

11x/990 + 22x/990 + 33x/990 + ...+ 99x/990 = (11x + 22x + 33x +...+ 99x)/990

11x + 22x + 33x + ...+ 99x = 110 + x + 220 + x + 330 + x + ...+ 990 + x

= 9x + 110 + 220 + 330 + ...+ 990

= 9*x + 4950

11x/990 + 22x/990 + 33x/990 + ...+ 99x/990 = (11x + 22x + 33x +...+ 99x)/990 = (9*x + 4950)/990 = 9*x/990 + 4950/990

_________________

9*x/990 + 4950/990 - 45/990 = 4923/990

9*x/990 + 4905/990 = 4923/990

9*x/990 = 4923/990 - 4905/990 = 18/990

9*x = 18

x = 18 : 2 = 9

________________

11x, 22x, 33x, ..., 99x le scrii cu bara deasupra.