Răspuns:
R:a)9 b)17
Explicație pas cu pas:
13. Determinati cifra x din egalităţile:
a)0,(xl)+0,(x2)+0,(x3) +...+0,(x8)=7,(63)
7,(63)=7 63/99=7 21/33=7 7/11=84/11
x1/99+x2/99+...+x8/99=84/11
[80x×(1+2+...+8)]/99=84/11
1+2+3+...+8=8×9/2=72/2=36
(80x+36)/99=84/11
(80x+36)/99=84/11 /×11
(80x+36)/9=84
80x+36=756
80x=756-36=720
x=720/80
x=9
b) 0,0(x)+0,1(x) +0,2(x) +0,3(x) +0,4(x)
+0,5(x)=1,9(6).
x/90+(1x-1)/90+(2x-2)/90+(3x-3)/90+
(4x-4)/90=1 (96-9)/90
(11x-10)/90=1 87/90
(11x-10)/90=1 29/30
(11x-10)/90=59/30 /30
(11x-10)/3=59
11x-10=59×3
11x=177+10
11x=187 /:11
x=17.
