Giải:

Ta có: \(\frac{a}{2}=\frac{b}{5}\Rightarrow\frac{a}{8}=\frac{b}{20}\)

\(\frac{b}{4}=\frac{c}{3}\Rightarrow\frac{b}{20}=\frac{c}{15}\)

\(\Rightarrow\frac{a}{8}=\frac{b}{20}=\frac{c}{15}\)

Đặt \(\frac{a}{8}=\frac{b}{20}=\frac{c}{15}=k\)

\(\Rightarrow a=8k,b=20k,c=15k\)

Mà \(ab-c^2=-10,4\)

\(\Rightarrow8k20k-\left(15k\right)^2=-10,4\)

\(\Rightarrow160k^2-15^2.k^2=-10,4\)

\(\Rightarrow\left(160-15^2\right).k^2=-10,4\)

\(\Rightarrow-65.k^2=-10,4\)

\(\Rightarrow k^2=0,16\)

\(\Rightarrow k=\pm0,4\)

+) \(k=0,4\Rightarrow a=3,2;b=8;c=6\)

+) \(k=-0,4\Rightarrow a=-3,2;b=-8;c=-6\)

Vậy bộ số \(\left(a;b;c\right)\) là \(\left(3,2;8;6\right);\left(-3,2;-8;-6\right)\)

\(a\div b=2\div5\Rightarrow a=\frac{2}{5}b\)

\(b\div c=4\div3\Rightarrow c=\frac{3}{4}b\)

\(ab-c^2=-10,4\)

\(\Leftrightarrow\frac{2}{5}b.b-\left(\frac{3}{4}b\right)^2=-10,4\)

\(\Leftrightarrow\frac{-13}{80}b^2=-10,4\)

\(\Leftrightarrow b^2=64\)

\(\Leftrightarrow\orbr{\begin{cases}b=8\Rightarrow a=\frac{16}{5},c=6\\b=-8\Rightarrow a=\frac{-16}{5},c=-6\end{cases}}\)

\(\left|a+b+c\right|=\left|8+\frac{16}{5}+6\right|=\frac{86}{5}=17,2\)

=17,2 hok tốt

\(a:b=2:5\Rightarrow\frac{a}{2}=\frac{b}{5}\Rightarrow\frac{a}{8}=\frac{b}{20}\left(1\right)\)

\(b:c=4:3\Rightarrow\frac{b}{4}=\frac{c}{3}\Rightarrow\frac{b}{20}=\frac{c}{15}\left(2\right)\)

Từ (1) và (2) 

=> \(\frac{a}{8}=\frac{b}{20}=\frac{c}{15}\)

Đặt \(\frac{a}{8}=\frac{b}{20}=\frac{c}{15}=k\)

\(\Rightarrow\hept{\begin{cases}a=8k\\b=20k\\c=15k\end{cases}}\)

Thay a,b,c vào đẳng thức :

=> ab - c² = 160k² - 225k² = -10,4

=> -65k = -10,4

=> k = \(-\frac{4}{25}\)

\(\Rightarrow\hept{\begin{cases}a=8k=-\frac{32}{25}\\b=20k=-\frac{16}{5}\\c=15k=-\frac{12}{5}\end{cases}}\)

\(\Rightarrow\left|a+b+c\right|=\left|\frac{-32}{25}+\frac{-16}{5}+\frac{-12}{5}\right|=\frac{172}{25}=6,88\)

Cảm ơn nhé!

= 215/38 nhé bạn a=20/19; b=50/19; c=75/38

Ta có a:b=3:5=> \(\frac{a}{3}=\frac{b}{5}\left(1\right)\)

Lại có b:c=1:2=>\(\frac{b}{1}=\frac{c}{2}=>\frac{b}{5}=\frac{c}{10}\left(2\right)\)

Từ (1) và (2) => \(\frac{a}{3}=\frac{b}{5}=\frac{c}{10}=\frac{a+b+c}{3+5+10}=\frac{180}{18}=10\)

=> \(\hept{\begin{cases}a=30\\b=50\\c=100\end{cases}}\)

a : b = 3 : 5 

=> a = \(\frac{3}{5}b\)

b : c = 1 ; 2 

=> c = \(2b\)

Mà a + b + c = 180

=> \(\frac{3}{5}b\)+ b + 2b = 180

=> \(\left(\frac{3}{5}+1+2\right)b=180\)

=> \(\frac{18}{5}b=180\)

=> \(b=50\)

=> a = \(\frac{3}{5}b=\frac{3}{5}.50=30\)

     c = 2b = 2 . 50 = 100

Vậy a = 30 ; b = 50 ; c = 100