Ta có: \(15a=10b=6c\Rightarrow\dfrac{15a}{30}=\dfrac{10b}{30}=\dfrac{6c}{30}\Rightarrow\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{5}\)
Đặt \(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{5}=k\) \(\left(k\ne0\right)\)
\(\Rightarrow\left\{{}\begin{matrix}a=2k\\b=3k\\c=5k\end{matrix}\right.\)
Ta có: \(abc=-1920\Rightarrow2k\times3k\times5k=-1920\Rightarrow\left(2\times3\times5\right)\times\left(k\times k\times k\right)=-1920\Rightarrow30k^3=-1920\Rightarrow k^3=-1920\div30\Rightarrow k^3=-64\Rightarrow k=-4\)
\(\Rightarrow\left\{{}\begin{matrix}a=2\times\left(-4\right)\\b=3\times\left(-4\right)\\c=5\times\left(-4\right)\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a=-8\\b=-12\\c=-20\end{matrix}\right.\)
\(\Rightarrow K=\left|a+b+c\right|=\left|\left(-8\right)+\left(-12\right)+\left(-20\right)\right|=\left|-40\right|=40\)
Vậy giá trị của biểu thức \(K=\left|a+b+c\right|\) bằng \(40\).
a = -8
b=-12
c=-20
|a+b+c|=|-8+(-12)+(-20)|=40
Bao giờ có thời gian rảnh mk lm cho!
a= -8
b = -12
c= -20
|a+b+c| = |-18+(-12)+(-20)|= 40