Question

4a-3b/2=5b-4c/3=3c-5a/4 chứng minh rằng a/3=b/4=c/5

Answer 1

Ta có : \(\dfrac{4a-3b}{2}=\dfrac{5b-4c}{3}=\dfrac{3c-5a}{4}\)

\(\Leftrightarrow\dfrac{20a-15b}{10}=\dfrac{15b-12c}{9}=\dfrac{12c-20a}{16}=\dfrac{20a-15b+15b-12c+12c-20a}{10+9+16}=0\)\(\Leftrightarrow\left\{{}\begin{matrix}4a-3b=0\\5b-4c=0\\3c-5a=0\end{matrix}\right.\) 

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{a}{3}=\dfrac{b}{4}\\\dfrac{b}{4}=\dfrac{c}{5}\\\dfrac{c}{5}=\dfrac{a}{3}\end{matrix}\right.\Leftrightarrow\dfrac{a}{3}=\dfrac{b}{4}=\dfrac{c}{5}\)