3a = 2b = > 6a = 4b ; 4b = 5c
=> 6a = 4b = 5c
=> 6a/60 = 4b/60 = 5c/60
=> a/10 = b/15 = c/12
=> -a/-10 = b/15 = c/12
=> (-a - b + c)/(-10 - 15 + 12) = a/10 = b/15 = c/12
=> -52/-13 = a/10 = b/15 = c/12
=> 4 = a/10 = b/15 = c/12
=> x = 40; b = 60; c = 48
\(3a=2b;4b=5c\)và \(-a-b+c=-52\)
Theo bài ra ta cs
\(+,3a=2b\Rightarrow\frac{a}{2}=\frac{b}{3}\)
\(+,4b=5c\Rightarrow\frac{b}{5}=\frac{c}{4}\)
Ta lại cs :
\(+,\frac{a}{2}=\frac{b}{3}\Rightarrow\frac{a}{10}=\frac{b}{15}\)(1)
\(+,\frac{b}{5}=\frac{c}{4}\Rightarrow\frac{b}{15}=\frac{c}{12}\)(2)
Từ (1) và (2) \(\Rightarrow\frac{a}{10}=\frac{b}{15}=\frac{c}{12}\)
ADTC dãy tỉ số bằng nhau ta cs
\(\frac{a}{10}=\frac{b}{15}=\frac{c}{12}=\frac{-a-b+c}{-10-15+12}=-\frac{52}{-13}=4\)
\(\Rightarrow\hept{\begin{cases}\frac{a}{10}=4\\\frac{b}{15}=4\\\frac{c}{12}=4\end{cases}\Rightarrow\hept{\begin{cases}a=4.10=40\\b=4.15=60\\c=4.12=48\end{cases}}}\)