Vì 2a = 3b nên \(\dfrac{a}{3}=\dfrac{b}{2}\Leftrightarrow\dfrac{a}{21}=\dfrac{b}{14}\); 5a=7c nên \(\dfrac{a}{7}=\dfrac{c}{5}\Leftrightarrow\dfrac{a}{21}=\dfrac{c}{15}\)
\(\Rightarrow\dfrac{a}{21}=\dfrac{b}{14}=\dfrac{c}{15}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\Rightarrow\dfrac{a}{21}=\dfrac{b}{14}=\dfrac{c}{15}=\dfrac{a+b-c}{21+14-15}=\dfrac{50}{20}=\dfrac{5}{2}\)
\(\Leftrightarrow a=\dfrac{5}{2}\cdot21=52,5\\ b=\dfrac{5}{2}\cdot14=35\\ c=\dfrac{5}{2}\cdot15=37,5\)
2a=3b;5a=7c và a+b-c=50
⇒\(\dfrac{b}{2}=\dfrac{a}{3};\dfrac{c}{5}=\dfrac{a}{7}\) và a+b-c=50
⇒\(\dfrac{b}{2}=\dfrac{a}{3}\)⇒\(\dfrac{b}{14}=\dfrac{a}{21}\)
⇒\(\dfrac{c}{5}=\dfrac{a}{7}\)⇒\(\dfrac{c}{15}=\dfrac{a}{21}\)
Suy ra
\(\dfrac{a}{21}=\dfrac{b}{14}=\dfrac{c}{15}\)
⇒\(\dfrac{a}{21}=\dfrac{b}{14}=\dfrac{c}{15}=\dfrac{a+b-c}{21+14-15}=\dfrac{50}{20}=\dfrac{5}{2}\)
a=\(\dfrac{21.5}{2}=52,5\)
⇒ b=\(\dfrac{14.5}{2}=35\)
c=\(\dfrac{15.5}{2}=37,5\)
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