Question

sa se rezolve 0,(1×)+0,(2×)+...+0,(9×)=×

Answer 1

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

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

Answer 2

0,(1x)+0,(2x)+.....+0,(9x)=x
1x /99+2x/99+.....+9x/99=x/1
1x+2x+......+9x/99=99x/99
1x+2x+.....+9x=99x
10+x+20+x+......+90+x=99x
10*(1+2+....+9)+9x=99x
10*9*10:2=99x-9x
10*9*5=90x
10*45=90x
450=90x
x=450:90
x=5