a/c=b/d=3a/3c=4b/4d=5a/5c=6b/6d=3a+4b/3c+4d=5a-6b/5c-6d

3a+4b/3c+4d=5a-6b/5c-6d =>

3a+4b/5a-6b=3c+4d/5c-6d

trang mấy

từ tỉ lệ thức đã cho

=>(3a+4b)(5c-6d)=(3c+4d)(5a-6b)

=>15ac-18ad+20bc-24bd=15ac+20ad-18bc-24bd

=>-18ad+20bc=20ad-18bc

=>-18ad-20ad=-18bc-20bc

=>-38ad=-38bc

=>ad=bc

=>a/b=c/d

=>

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

\(\Leftrightarrow\dfrac{a}{\dfrac{3}{2}}=\dfrac{b}{\dfrac{4}{3}}=\dfrac{c}{\dfrac{5}{4}}\)

mà a+b-c=38

nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{a}{\dfrac{3}{2}}=\dfrac{b}{\dfrac{4}{3}}=\dfrac{c}{\dfrac{5}{4}}=\dfrac{a+b-c}{\dfrac{3}{2}+\dfrac{4}{3}-\dfrac{5}{4}}=\dfrac{38}{\dfrac{19}{12}}=24\)

Do đó:

\(\left\{{}\begin{matrix}\dfrac{a}{\dfrac{3}{2}}=24\\\dfrac{b}{\dfrac{4}{3}}=24\\\dfrac{c}{\dfrac{5}{4}}=24\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=24\cdot\dfrac{3}{2}=36\\b=24\cdot\dfrac{4}{3}=32\\c=24\cdot\dfrac{5}{4}=30\end{matrix}\right.\)

Vậy:(a,b,c)=(36;32;30)

\(\dfrac{3a+4b}{5a-6b}=\dfrac{3c+4d}{5c-6d}\)

=> \(\dfrac{3a+4b}{3c+4d}=\dfrac{5a-6b}{5c-6d}\)

ta có

\(\dfrac{3a+4b}{3c+4d}=\dfrac{3a}{3c}=\dfrac{4b}{4d}=\dfrac{a}{c}=\dfrac{b}{d}=>\dfrac{a}{b}=\dfrac{c}{d}\)(đpcm)

Ta có:

\(\dfrac{3a+4b}{5a-6b}=\dfrac{3c+4d}{5c-6d}\)

\(\Leftrightarrow\left(3a+4b\right)\left(5c-6d\right)=\left(3c+4d\right)\left(5a-6b\right)\)

\(\Rightarrow15ac-18ad+20bc-24bd=15ac-18bc+20ad-24bd\)

\(\Rightarrow15ac-15ac-18ad-20ad=-24bd+24bd-18bc-20bc\)

\(\Rightarrow-38ad=-38bc\)

\(\Rightarrow ad=bc\)

\(\Rightarrow\dfrac{a}{b}=\dfrac{c}{d}\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{a}{2}=\dfrac{b}{3}\\\dfrac{b}{5}=\dfrac{c}{4}\end{matrix}\right.\Leftrightarrow\dfrac{a}{10}=\dfrac{b}{15}=\dfrac{c}{12}\)

Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{a}{10}=\dfrac{b}{15}=\dfrac{c}{12}=\dfrac{a-b+c}{10-15+12}=\dfrac{-56}{7}=-8\)

Do đó: a=-80; b=-120; c=-96