Ta có:
\(\left\{{}\begin{matrix}\dfrac{a}{2}=\dfrac{b}{5}\\\dfrac{b}{4}=\dfrac{c}{7}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\dfrac{a}{8}=\dfrac{b}{20}\\\dfrac{b}{20}=\dfrac{c}{35}\end{matrix}\right.\Rightarrow\dfrac{a}{8}=\dfrac{b}{20}=\dfrac{c}{35}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{a}{8}=\dfrac{b}{20}=\dfrac{c}{35}=\dfrac{2a-b+c}{8.2-20+35}=\dfrac{31}{31}=1\)
\(\left\{{}\begin{matrix}a=1.8=8\\b=1.20=20\\c=1.35=35\end{matrix}\right.\)
Vậy............
Chúc bạn học tốt!!!
ta có : \(\dfrac{a}{2}=\dfrac{b}{5}\Leftrightarrow2b=5a\Leftrightarrow14b=35avàb=\dfrac{5}{2}a\) (1)
\(\dfrac{b}{4}=\dfrac{c}{7}\Leftrightarrow7b=4c\Leftrightarrow14b=8c\)
\(\Rightarrow8c=35a\Leftrightarrow c=\dfrac{35}{8}a\) (2)
thay (1);(2)vào \(2a-b+c=31\Leftrightarrow2a-\dfrac{5}{2}a+\dfrac{35}{8}a=31\)
\(\Leftrightarrow\dfrac{31}{8}a=31\Leftrightarrow a=\dfrac{31}{\dfrac{31}{8}}=8\)
\(\Rightarrow\dfrac{8}{2}=\dfrac{b}{5}\Leftrightarrow b=\dfrac{8}{2}.5=\dfrac{40}{2}=20\)
\(\Rightarrow\dfrac{20}{4}=\dfrac{c}{7}\Leftrightarrow c=\dfrac{20}{4}.7=35\)
vậy \(a=8;b=20;c=35\)
