Có :
\(\dfrac{a}{2}=\dfrac{b}{4}=\dfrac{c}{5}=\dfrac{5a}{10}=\dfrac{b}{4}=\dfrac{3c}{15}=\dfrac{5a-b+3c}{10-4+15}=\dfrac{42}{21}=2\)
( do \(5a-b+3c=42\) )
Suy ra :
\(\dfrac{5a}{10}=2\Rightarrow\dfrac{a}{2}=2\Rightarrow a=4\)
\(\dfrac{b}{4}=2\Rightarrow b=8\)
\(\dfrac{3c}{15}=2\Rightarrow\dfrac{c}{5}=2\Rightarrow c=10\)
Vậy ....
Theo t/c dãy tỉ số bằng nhau ta có :
\(\dfrac{a}{2}=\dfrac{b}{4}=\dfrac{c}{5}=\dfrac{5a}{10}=\dfrac{b}{4}=\dfrac{3c}{15}=\dfrac{5a-b+3c}{10-4+15}=\dfrac{42}{21}=2\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a}{2}=2\Rightarrow a=2.2=4\\\dfrac{b}{4}=2\Rightarrow b=2.4=8\\\dfrac{c}{5}=2\Rightarrow5.2=10\end{matrix}\right.\)
Vậy...............................
vì\(\dfrac{a}{2}\)=\(\dfrac{b}{4}\)=\(\dfrac{c}{5}\)=>\(\dfrac{5a}{10}\)=\(\dfrac{b}{4}\)=\(\dfrac{3c}{15}\)
áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{5a}{10}\)=\(\dfrac{b}{4}\)=\(\dfrac{3c}{15}\)=\(\dfrac{5a-b+3c}{10-4+15}\)=\(\dfrac{42}{21}\)=2
vì\(\dfrac{5a}{10}\)=2=>5a=2*10=20=>a=20:5=4
\(\dfrac{b}{4}\)=2=>b=2*4=8
\(\dfrac{3c}{15}\)=2=>3c=2*15=30=>c=30:3=10
vậy a=4,b=8,c=10
