\(\dfrac{1}{2a-1}=\dfrac{2}{3b-1}=\dfrac{3}{4c-1}\Rightarrow\dfrac{2a-1}{1}=\dfrac{3b-1}{2}=\dfrac{4c-1}{3}\)
\(\Rightarrow\dfrac{36a-18}{18}=\dfrac{24b-8}{16}=\dfrac{12c-3}{9}\)và 3a+2b-c=4
Áp dụng t/c dãy tỉ số bằng nhau:
\(\dfrac{36a-18}{18}=\dfrac{24b-8}{16}=\dfrac{12c-3}{9}=\dfrac{36a-18+24b-8-12c+3}{18+16-9}=\dfrac{12\left(3a+2b-c\right)-23}{25}=\dfrac{12\cdot4-23}{25}=1\)
=>2a-1=1<=>a=1
3b-1=2<=>b=1
4c-1=3<=>c=1
Vậy...
\(\dfrac{1}{2a-1}=\dfrac{2}{3b-1}=\dfrac{3}{4c-1}\\ \Rightarrow\dfrac{2a-1}{1}=\dfrac{3b-1}{2}=\dfrac{4c-1}{3}\\ \Rightarrow\dfrac{36a-18}{18}=\dfrac{24b-8}{16}=\dfrac{12c-3}{9}=\dfrac{36a-18+24b-8-12c+3}{18+16-9}=\dfrac{12\left(3a+2b-c\right)-23}{25}\\ =\dfrac{12.4-23}{25}=1\\ \Rightarrow a=1;b=1;c=1\)
