a:b=2:5; b:c=4:3=>\(\frac{a}{2}=\frac{b}{5};\frac{b}{4}=\frac{c}{3}\Rightarrow\frac{a}{8}=\frac{b}{20}=\frac{c}{15}\)

Đặt \(k=\frac{a}{8}=\frac{b}{20}=\frac{c}{15}\Rightarrow k^2=\frac{a.b}{8.20}=\frac{c^2}{225}\)

Áp dụng tính chất dãy tỉ số bằng nhau,ta có:

\(k^2=\frac{a.b}{160}=\frac{c^2}{225}=\frac{a.b-c^2}{160-225}=\frac{-10,4}{-65}=0,16\)

\(\Rightarrow\left[\begin{array}{nghiempt}k=0,4\\k=-0,4\end{array}\right.\)

Với k=0,4=>a=3,2; b=8; c=6=>|a+b+c|=17,2

Với k=-0,4 =>a=-3,2; b=-8; c=-6=>|a+b+c|=17,2

Vậy|a+b+c|=17,2

17,2

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

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

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

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

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

\(\Leftrightarrow b^2=64\)

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

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

=17,2 hok tốt

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 \(\left(3,2;8;6\right);\left(-3,2;-8;-6\right)\)

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

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

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

a:b=b:c=c:a=>a/b=b/c=c/a=a+b+c/b+c+a=1

suy ra: a/b=1 suy ra: a=b

b/c=1 =>b=c

suy ra: a=b=c

suy ra: a^2.b^2.c^1930:b^1935=1.1.1:1=1