Question

Daca ati putea sa ma ajutati cu exercitiile 14 si 15, va rog!! Dau coroana!!

Answer 1

Răspuns:

Explicație pas cu pas:

14)

Fie $n=2k$, atunci:

$a=\frac{2}{3} -\frac{3}{4} +\frac{5}{6} =\frac{3}{4}$

$|a|=|\frac{3}{4} }|=\frac{3}{4}$

Pentru $n=2k+1$ obținem:

$a=-\frac{2}{3}+\frac{3}{4}-\frac{5}{6} =\frac{-3}{4}$

$|a|=|-\frac{3}{4} |=\frac{3}{4}$

15)

$\begin{aligned}&=\frac{\overline{a, b(c)}+\overline{b, c(a)}+\overline{a, b(c)}}{a+b+c} \Rightarrow 10 x=\frac{\overline{a b,(c)}+\overline{b c,(a)}+\overline{a b,(c)}}{a+b+c}= \\&=\frac{\overline{a b}+0,(c)+\overline{b c}+0,(a)+\overline{c a}+0,(b)}{a+b+c}= \\&=\frac{10 a+b+\frac{c}{9}+10 b+c+\frac{a}{g}+10 c+a+\frac{b}{g}}{a+b+c}=\end{aligned}$

$\begin{aligned}&=\frac{11 a+11 b+11 c+\frac{a+b+c}{g}}{a+b+c}=\frac{11(a+b+c)+\frac{a+b+c}{g}}{a+b+c} \\&=\frac{(a+b+c)\left(11+\frac{1}{g}\right)}{a+b+c}=\frac{100}{9} \\&10 x=\frac{100}{9} \Rightarrow x=\frac{10}{9} \\&9 x=9 \cdot \frac{10}{9}=10 \in \mathbb{N}\end{aligned}$