Question

solutia ecuatiei 0,(1x1) +0,(2x2)+...+0,(9x9)=x este..

Answer 1

0,(1x1) +0,(2x2)+...+0,(9x9)=x
(101+10x)/999+(202+10x)/999+.....+(909+10x)/999=x
101+10x+202+10x+.....+909+10x=999x
101(1+2+....+9)+10x×9 =999x
101×9×10/2+90x=999x
909×5=909x
x=5

Answer 2

Inmultim cu 1000
1x1 + 2x2 +...+9x9=1000x
(100+200+...+900)+90x+(1+2+...+9)=1000x
(101+202+...+909)+90x=1000x
101(1+2+...+9)+90x=1000x
101*9*10/2=910x
101*9/2=91x

x=909/182=5    (4,994......)