theo đề,ta có:\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{d}{5}vớia+b+c+d=-42\)
theo tính chất của dãy tỉ số bằng nhau,ta có:
\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{d}{5}=\dfrac{a+b+c+d}{2+3+4+5}=\dfrac{-24}{14}=-3\)
do đó:
\(\dfrac{a}{2}=-3=>a=-3.2=-6\)
\(\dfrac{b}{3}=-3=>b=-3.3=-9\)
\(\dfrac{c}{4}=-3=>c=-3.4=-12\)
\(\dfrac{d}{5}=-3=>d=-3.5=-15\)
vậy a=-6
b=-9
c=-12
d=-15
\(\text{Theo bài ra ta có : }a:b:c:d=2:3:4:5\\ \Rightarrow\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{d}{5}\\ a+b+c+d=-42\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được :
\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{d}{5}=\dfrac{a+b+c+d}{2+3+4+5}=\dfrac{-42}{14}=-3\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a}{2}=-3\\\dfrac{b}{3}=-3\\\dfrac{c}{4}=-3\\\dfrac{d}{5}=-3\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a=-6\\b=-9\\c=-12\\d=-15\end{matrix}\right.\)
Vậy \(a=-6;b=-9;c=-12;d=-15\)
\(\Rightarrow\)\(\dfrac{a}{2}\) =\(\dfrac{b}{3}\)=\(\dfrac{c}{4}\)=\(\dfrac{d}{5}\) Và a +b +c + d =-42
\(\dfrac{a}{2}\) = \(\dfrac{b}{3}\)=\(\dfrac{c}{4}\)= \(\dfrac{d}{5}\)=\(\dfrac{a+b+c+d}{2+3+4+5}\)=\(\dfrac{-42}{14}\)=-3
⇒\(\dfrac{a}{2}\) =\(\dfrac{b}{3}\)=\(\dfrac{c}{4}\)=\(\dfrac{d}{5}\)Và a +b +c + d =-42
\(\dfrac{a}{2}\) = \(\dfrac{b}{3}\)=\(\dfrac{c}{4}\)=\(\dfrac{d}{5}\) =\(\dfrac{a+b+c+d}{2+3+4+5}\)= \(\dfrac{-42}{14}\)= 3
Vậy A=6,B=9,C=12,D=15
