Question

si asta trebuie facuta o uitasem

Answer 1

$\overline{0,(1x)}\to \frac{10+x}{99} = \frac{10}{99}+\frac{x}{99} \\\\ \overline{0,(2x)}\to \frac{20+x}{99}=\frac{20}{99}+\frac{x}{99} .\\.\\.\\. \\\\ \overline{0,(9x)}\to \frac{90+x}{99}=\frac{90}{99}+\frac{x}{99} \\\\\\ \frac{x}{99}+\frac{10}{99}+\frac{x}{99}+\frac{20}{99}+....+ \frac{x}{99}+\frac{90}{99}=x \\\\ \not 9* \frac{x}{\not 99}+ \frac{10+20+...+90}{99}=x \\\\ \frac{x}{11}+ \frac{\not10*\frac{(1+9)*9}{\not2}}{99}=x \\\\ \frac{x}{11} + \frac{5*10* \not 9}{\not 99}=x \\\\ \frac{x+50}{11}=x$

$x+50=11x \\\\ x-11x=-50 \\\\ -10x=-50 \ \ \ |:(-10) \\\\ \boxed{x=5}$