Ta thất:15a=10b=6c
\(\Rightarrow\frac{a}{10}=\frac{b}{15},\frac{b}{6}=\frac{c}{10}\)
\(\Rightarrow\frac{a}{20}=\frac{b}{30}\),\(\frac{b}{30}=\frac{c}{50}\)
Đặt a=29k,b=30k,c=50k
Mà abc=-1920\(\Leftrightarrow k^3=\frac{-8}{125}\)
\(\Leftrightarrow k=\frac{-2}{5}\)
\(\Leftrightarrow\hept{\begin{cases}a=20k=-8\\b=30k=-12\\c=50k=-20\end{cases}}\)
ta có: 15a=10ob=6c
Suy ra a/10=b/15 ; b/6=c/10
Suy ra a/20=b/30 ;b/30=c/50 suy ra a/20=b/30=c/50
Đặt: a/20=b/30=c/50=k
Suy ra a=20k;=30k;c=50k
Mà a,b,c=-1920
20k.30k.50k=-1920
k^3=-8/125 suy ra k=-2/5
suy ra a=20k=-8, b=30k=-12, c=50k=-20
Ta có: \(15a=10b=6c\)
\(\Rightarrow\left(15a\right)^3=15a.10b.6c\)
\(\Rightarrow3375a^3=\left(15.10.6\right).\left(a.b.c\right)\)
\(\Rightarrow3375a^3=900.\left(-1920\right)\)
\(\Rightarrow3375a^3=-1728000\)
\(\Rightarrow a^3=\frac{-1728000}{3375}=-512\)
\(\Rightarrow a=-8\)
Ta lại có: \(\hept{\begin{cases}10b=15a\\6c=15a\end{cases}\Rightarrow\hept{\begin{cases}10b=-120\\6c=-120\end{cases}\Rightarrow}\hept{\begin{cases}b=-12\\c=-20\end{cases}}}\)
Vậy \(a=-8;b=-12\text{ và }c=-20\)
\(15a=10b=6c\)
\(\Rightarrow\frac{15a}{30}=\frac{10b}{30}=\frac{6c}{30}\)
\(\Rightarrow\frac{a}{2}=\frac{b}{3}=\frac{c}{5}\)
Đặt \(\frac{a}{2}=\frac{b}{3}=\frac{c}{5}=k\)
\(\Rightarrow a=2k;b=3k,c=5k\)
Ta có
\(abc=-1920\)
\(\Rightarrow30k^3=-1920\)
\(\Rightarrow k^3=-64\)
\(\Rightarrow k=-4\)
Thay vào tính đảm bào OK.
