Từ \(3a=4b=6c\Rightarrow\dfrac{a}{\dfrac{1}{3}}=\dfrac{b}{\dfrac{1}{4}}=\dfrac{c}{\dfrac{1}{6}}\)\(\Rightarrow\dfrac{a}{\dfrac{1}{3}}=\dfrac{2b}{\dfrac{1}{2}}=\dfrac{c}{\dfrac{1}{6}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{a}{\dfrac{1}{3}}=\dfrac{2b}{\dfrac{1}{2}}=\dfrac{c}{\dfrac{1}{6}}=\dfrac{2b-a+c}{\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{6}}=\dfrac{10}{\dfrac{1}{3}}=30\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a}{\dfrac{1}{3}}=30\Rightarrow a=30\cdot\dfrac{1}{3}=10\\\dfrac{2b}{\dfrac{1}{2}}=30\Rightarrow b=\dfrac{30\cdot\dfrac{1}{2}}{2}=\dfrac{15}{2}\\\dfrac{c}{\dfrac{1}{6}}=30\Rightarrow c=30\cdot\dfrac{1}{6}=5\end{matrix}\right.\)
Ta có:
3a = 4b = 6c \(\Rightarrow\) \(\dfrac{3a}{12}=\dfrac{4b}{12}=\dfrac{6c}{12}\)
\(\Rightarrow\) \(\dfrac{a}{4}=\dfrac{b}{3}=\dfrac{c}{2}\)
\(\Rightarrow\) \(\dfrac{a}{4}=\dfrac{2b}{6}=\dfrac{c}{2}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\dfrac{a}{4}=\dfrac{2b}{6}=\dfrac{c}{2}=\dfrac{2b-a+c}{6-4+2}=\dfrac{10}{4}=2,5\)
Suy ra:
\(\dfrac{a}{4}=2,5\Rightarrow\)a = 10
\(\dfrac{2b}{6}=2,5\Rightarrow2b=15\Rightarrow b=\dfrac{15}{2}=7,5\)
\(\dfrac{c}{2}=2,5\Rightarrow c=5\)
Vậy a = 10 ; b = 7,5 ; c = 5
ta có:
3a=4b=6c
\(\Rightarrow\dfrac{3a}{12}=\dfrac{4b}{12}=\dfrac{6c}{12}\) \(\Rightarrow\dfrac{a}{4}=\dfrac{b}{3}=\dfrac{c}{2}\) \(\Rightarrow\dfrac{2b}{6}=\dfrac{a}{4}=\dfrac{c}{2}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\dfrac{2b}{6}=\dfrac{a}{4}=\dfrac{c}{2}=\dfrac{2b-a+c}{6-4+2}=\dfrac{10}{4}=\dfrac{5}{2}\) (vì 2b-a+c=10)
\(\Rightarrow\left\{{}\begin{matrix}a=7,5\\b=10\\c=5\end{matrix}\right.\)