Question

aflati cifra x din egalitatea 0,(x1)+0,(x2)+....+0,(x9)=x

Answer 1

$\it 0,(\overline{x1}) + 0,(\overline{x2})+0,(\overline{x3})+ ... +0,(\overline{x9}) =x$

$\it \dfrac{\overline{x1}}{99} + \dfrac{\overline{x2}}{99} + \dfrac{\overline{x3}}{99} + ... + \dfrac{\overline{x9}}{99} + =x$

$\it \dfrac{1}{99}( \ \overline{x1}+\overline{x2}+\overline{x3}+ ... +\overline{x9})=x$

$\it 10x+1 +10x+2 +10x+3 + ...+10x+9 = 99x$

$\it 9\cdot10x +(1+2+3+ ...+9) = 99x$

$\it 90x +45 = 99x \Longrightarrow 45 = 99x - 90x \Longrightarrow 45 = 9x \Longrightarrow x = 5 .$