Question

Va rog !!! Dau coroana !!!​

Answer 1

x1/99+1 x2/99+2 x3/99+...+8 x9=x+36

1/99(x1+99+x2+2×99+x3+

+8×99+x9)=x+36

x1+x2+x3+...+x9+99(1+2+3+..+8)=

99x+36×99

10x+1+19x+2+..

90x+45+99×36=99x+36×99/-99×36

90x+45=99x

9x=45

x=5

Answer 2

Răspuns:

5

Explicație pas cu pas:

$\overline {0,(x1)} + \overline {1,(x2)} + \overline {2,(x3)} + ... + \overline {8,(x9)} = x + 36 \\ \frac{\overline {x1}}{99} + \frac{\overline {1x2} - 1}{99} + \frac{\overline {2x3} - 2}{99} + ... + \frac{\overline {8x9} - 8}{99} = x + 36$

$10x + 1 + 100 + 10x + 2 - 1 + 200 + 10x + 3 - 2 + ... + 800 + 10x + 9 - 8 = 99(x + 36)$

$9 \cdot 10x + 9 + 100(1 + 2 + ... + 8) = 99(x + 36)$

$90x + 9 + \frac{100 \cdot 8 \cdot 9}{2} = 99(x + 36) \\ 9(10x + 1 + 400) = 99(x + 36) \\ 10x + 401 = 11x + 396 \implies \bf x = 5$