\(2a=3b;5b=7c\Rightarrow\dfrac{a}{3}=\dfrac{b}{2};\dfrac{b}{7}=\dfrac{c}{5}\)
\(\Rightarrow\dfrac{a}{21}=\dfrac{b}{14};\dfrac{b}{14}=\dfrac{c}{10}\)
\(\Rightarrow\dfrac{a}{21}=\dfrac{b}{14}=\dfrac{c}{10}\)
áp dụng dãy tỉ số bằng nhau ta có:
\(\dfrac{a3+c5-b7}{21.5+10.5-14.7}=\dfrac{30}{15}=2\)
\(\Rightarrow a=2.21=42\)
\(b=14.2=28\)
\(c=10.2=20\)
Vì 5b = 7c => 7c - 5b = 0 Mà 7c - 5b = 3(a - 10) => 3(a-10) = 0 => a - 10 = 0 => a = 10 Vì 2a = 3b => 2.10 = 3b => b = \(\dfrac{20}{3}\) Vì 5b = 7c => c = \(\dfrac{5b}{7}\)= \(\dfrac{5.\dfrac{20}{3}}{7}\)= \(\dfrac{100}{21}\) Vậy a = 10 ; b = \(\dfrac{20}{3}\); c = \(\dfrac{100}{21}\)
