Ta có :
\(3a+5b-7c=30\)
\(2a=3b;5b=7c\)
\(\Leftrightarrow\dfrac{a}{3}=\dfrac{b}{2}\Leftrightarrow\dfrac{a}{21}=\dfrac{b}{14}\)
\(\Leftrightarrow\dfrac{b}{7}=\dfrac{c}{5}\Leftrightarrow\dfrac{b}{14}=\dfrac{c}{10}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\dfrac{a}{21}=\dfrac{b}{14}=\dfrac{c}{10}=\dfrac{3a+5b-7c}{3.21+14.5-10.7}=\dfrac{30}{63}=\dfrac{10}{21}\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{a}{21}=\dfrac{10}{21}\Leftrightarrow a=10\\\dfrac{b}{14}=\dfrac{10}{21}\Leftrightarrow b=\dfrac{140}{21}\\\dfrac{c}{10}=\dfrac{10}{21}\Leftrightarrow c=\dfrac{100}{21}\end{matrix}\right.\)
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Theo đề bài ta có:
\(2a=3b;5b=7c\)
\(\Rightarrow\dfrac{a}{3}=\dfrac{b}{2};\dfrac{b}{7}=\dfrac{c}{5}\)
\(\Rightarrow\dfrac{a}{21}=\dfrac{b}{14};\dfrac{b}{14}=\dfrac{c}{10}\)
\(\Rightarrow\dfrac{a}{21}=\dfrac{b}{14}=\dfrac{c}{10}\)
\(\Rightarrow\dfrac{3a}{63}=\dfrac{5b}{70}=\dfrac{7c}{70}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{3a}{63}=\dfrac{5b}{70}=\dfrac{7c}{70}\)
\(=\dfrac{3a+5b-7c}{63+70-70}=\dfrac{30}{63}=\dfrac{10}{21}\)
\(\Rightarrow\left\{{}\begin{matrix}a=\dfrac{10}{21}.21=10\\b=\dfrac{10}{21}.14=\dfrac{20}{3}\\c=\dfrac{10}{21}.10=\dfrac{100}{21}\end{matrix}\right.\)
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