\(\dfrac{a}{2}=\dfrac{2b}{3}=\dfrac{3c}{4}\)
\(\Leftrightarrow\dfrac{a}{12}=\dfrac{2b}{12}=\dfrac{3c}{12}\)
\(\Leftrightarrow\dfrac{a}{12}=\dfrac{b}{6}=\dfrac{c}{4}\)
Theo t,c dãy tỉ số bằng nhau ta có :
\(\dfrac{a}{12}=\dfrac{b}{6}=\dfrac{c}{4}=\dfrac{a-b}{12-6}=\dfrac{15}{6}=\dfrac{5}{2}\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{a}{12}=\dfrac{5}{2}\\\dfrac{b}{6}=\dfrac{5}{2}\\\dfrac{c}{4}=\dfrac{5}{2}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a=30\\b=15\\c=10\end{matrix}\right.\)
Vậy ..
\(\dfrac{1}{2}a=\dfrac{2}{3}b=\dfrac{3}{4}c\)
\(\Leftrightarrow\dfrac{1}{2}a.12=\dfrac{2}{3}b.12=\dfrac{3}{4}c.12\)
\(\Leftrightarrow6a=8b=9c\)
\(\Leftrightarrow\dfrac{6a}{72}=\dfrac{8b}{72}=\dfrac{9c}{72}\)
\(\Leftrightarrow\dfrac{a}{12}=\dfrac{b}{9}=\dfrac{c}{8}\)
Áp dụng dãy tỉ số bằng nhau và a-b=15 có:
\(\dfrac{a}{12}=\dfrac{b}{9}=\dfrac{c}{8}=\dfrac{a-b}{12-9}=\dfrac{15}{3}=5\)
\(\Rightarrow\left\{{}\begin{matrix}a=5.12=60\\b=5.9=45\\c=5.8=40\end{matrix}\right.\)
Vậy....
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{a}{\dfrac{1}{2}}=\dfrac{b}{\dfrac{2}{3}}=\dfrac{c}{\dfrac{3}{4}}=\dfrac{a-b}{\dfrac{1}{2}-\dfrac{2}{3}}=\dfrac{15}{\dfrac{-1}{6}}=-90\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a}{\dfrac{1}{2}}=-90\Rightarrow a=-45\\\dfrac{b}{\dfrac{2}{3}}=-90\Rightarrow b=-60\\\dfrac{c}{\dfrac{3}{4}}=-90\Rightarrow c=\dfrac{-135}{2}\end{matrix}\right.\)
