Question

Buna, as fi foarte recunoscatoare daca m ati ajuta, multumesc frumos​

Answer 1

$\frac{a}{0,1(6)}=\frac{b}{0,125}=\frac{c}{0,08(3)} \\ 12(ab+ac+bc)=13abc \\k=\frac{a}{1/6}=\frac{b}{1/8}=\frac{c}{1/12} \\ \Rightarrow 6a=8b=12c \ \Leftrightarrow \ 3a=4b=6c \\ \Rightarrow a=2c; \\ \Rightarrow 2b=3c \ \Rightarrow \ b=\frac{3c}{2} \\ \Rightarrow \ 12(2c\cdot\frac{3c}{2}+2c \cdot c+\frac{3c}{2}\cdot c)=13\cdot2c\cdot \frac{3c}{2} \cdot c \\ \Rightarrow 12c(3c+2c+\frac{3c}{2})=39c^3 \\ \Rightarrow 12(\frac{10c}{2}+\frac{3c}{2})=39c^2 \\ \Rightarrow 12 \cdot \frac{13c}{2}=39c^2$

$\Rightarrow 39c=6\cdot 13 \\ \Rightarrow 3c=6 \ \Longrightarrow \boxed{\bold{c=2}} \\ a=2c=2 \cdot 2 \\ \Rightarrow \boxed{\bold{a=4}} \\ b=\frac{3c}{2}=\frac{3 \cdot 2}{2} \\ \Rightarrow \boxed{\bold{b=3}}$