Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
vì 2a/3=3b/4=4c/5 nên để chia hết cho 3,4,5 ta phải có hàng đơn vị ghép vào chia hết cho các số
24/3=32/4=40/5 hoặc 27/3=36/4=45/5
vậy a=4 hoặc 7
b=2 hoặc 6
c=0 hoặc 5
a, Đặt \(\frac{a}{2}=\frac{b}{3}=\frac{c}{5}=k\)\(\Rightarrow a=2k\); \(b=3k\); \(c=5k\)
Ta có: \(B=\frac{a+7b-2c}{3a+2b-c}=\frac{2k+7.3k-2.5k}{3.2k+2.3k-5k}=\frac{2k+21k-10k}{6k+6k-5k}=\frac{13k}{7k}=\frac{13}{7}\)
b, Ta có: \(\frac{1}{2a-1}=\frac{2}{3b-1}=\frac{3}{4c-1}\)\(\Rightarrow\frac{2a-1}{1}=\frac{3b-1}{2}=\frac{4c-1}{3}\)
\(\Rightarrow\frac{2\left(a-\frac{1}{2}\right)}{1}=\frac{3\left(b-\frac{1}{3}\right)}{2}=\frac{4\left(c-\frac{1}{4}\right)}{3}\) \(\Rightarrow\frac{2\left(a-\frac{1}{2}\right)}{12}=\frac{3\left(b-\frac{1}{3}\right)}{2.12}=\frac{4\left(c-\frac{1}{4}\right)}{3.12}\)
\(\Rightarrow\frac{\left(a-\frac{1}{2}\right)}{6}=\frac{\left(b-\frac{1}{3}\right)}{8}=\frac{\left(c-\frac{1}{4}\right)}{9}\)\(\Rightarrow\frac{3\left(a-\frac{1}{2}\right)}{18}=\frac{2\left(b-\frac{1}{3}\right)}{16}=\frac{\left(c-\frac{1}{4}\right)}{9}\)
\(\Rightarrow\frac{3a-\frac{3}{2}}{18}=\frac{2b-\frac{2}{3}}{16}=\frac{c-\frac{1}{4}}{9}\)
Áp dụng tính chất dãy tỉ số bằng nhau, ta có:
\(\frac{3a-\frac{3}{2}}{18}=\frac{2b-\frac{2}{3}}{16}=\frac{c-\frac{1}{4}}{9}=\frac{3a-\frac{3}{2}+2b-\frac{2}{3}-\left(c-\frac{1}{4}\right)}{18+16-9}=\frac{3a-\frac{3}{2}+2b-\frac{2}{3}-c+\frac{1}{4}}{25}\)
\(=\frac{\left(3a+2b-c\right)-\left(\frac{3}{2}+\frac{2}{3}-\frac{1}{4}\right)}{25}=\left(4-\frac{23}{12}\right)\div25=\frac{25}{12}\times\frac{1}{25}=\frac{1}{12}\)
Do đó: +) \(\frac{a-\frac{1}{2}}{6}=\frac{1}{12}\)\(\Rightarrow a-\frac{1}{2}=\frac{6}{12}\)\(\Rightarrow a=1\)
+) \(\frac{b-\frac{1}{3}}{8}=\frac{1}{12}\)\(\Rightarrow b-\frac{1}{3}=\frac{8}{12}\)\(\Rightarrow b=1\)
+) \(\frac{c-\frac{1}{4}}{9}=\frac{1}{12}\)\(\Rightarrow c-\frac{1}{4}=\frac{9}{12}\)\(\Rightarrow c=1\)
ta có :
\(\frac{2a}{3}=\frac{3b}{4}=\frac{4c}{5}=\frac{12a}{18}=\frac{12b}{16}=\frac{12c}{15}=\frac{a}{18}=\frac{b}{16}=\frac{c}{15}\)
áp dụng tính chất dãy tỉ số bằng nhau, ta có :
\(\frac{a}{18}=\frac{b}{16}=\frac{c}{15}=\frac{a+b+c}{18+16+15}=\frac{49}{49}=1\)
\(\frac{a}{18}=1\Rightarrow a=18\)
\(\frac{b}{16}=1\Rightarrow b=16\)
\(\frac{c}{15}=1\Rightarrow c=15\)
ta có :
\(\frac{2a}{3}=\frac{3b}{4}=\frac{4c}{5}=\frac{12a}{18}=\frac{12b}{16}=\frac{12c}{15}=\frac{a}{18}=\frac{b}{16}=\frac{c}{15}\)
áp dụng tính chất dãy tỉ số bằng nhau, ta có :
\(\frac{a}{18}=\frac{b}{16}=\frac{c}{15}=\frac{a+b+c}{18+16+15}=\frac{49}{49}=1\)
\(\frac{a}{18}=1\Rightarrow a=18\)
\(\frac{b}{16}=1\Rightarrow b=16\)
\(\frac{c}{15}=1\Rightarrow c=15\)
Ta có: \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)
\(\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{2a}{2c}=\frac{3b}{3d}=\frac{2a+3b}{2c+3d}\left(1\right)\)
\(\Rightarrow\frac{2a}{2c}=\frac{3b}{3d}=\frac{2a-3b}{2a-3d}\left(2\right)\)
Từ (1) và (2)
\(\Rightarrow\frac{2a+3b}{2c+3d}=\frac{2a-3b}{2c-3d}\)
\(\Rightarrow\frac{2a+3b}{2a-3b}=\frac{2c+3d}{2c-3d}\left(đpcm\right)\)
a/ Với
\(\frac{3x-y}{x+y}=\frac{3}{4}=\frac{3\frac{x}{y}-1}{\frac{x}{y}+1}\Rightarrow3\left(\frac{x}{y}+1\right)=4\left(3\frac{x}{y}-1\right)\)
\(\Rightarrow3\frac{x}{y}+3=12\frac{x}{y}-4\Rightarrow9\frac{x}{y}=7\Rightarrow\frac{x}{y}=\frac{7}{9}\)
b/
\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{2a}{2c}=\frac{3b}{3d}=\frac{2a+3b}{2c+3d}=\frac{2a-3b}{2c-3d}\)
\(\Rightarrow\frac{2a+3b}{2c+3d}=\frac{2a-3b}{2c-3d}\Rightarrow\frac{2a+3a}{2a-3b}=\frac{2c+3d}{2c-3d}\)
Ta có :\(\frac{2a}{3}=\frac{3b}{4}=\frac{4c}{5}\)
\(\frac{a}{\frac{3}{2}}=\frac{b}{\frac{4}{3}}=\frac{2c}{\frac{5}{2}}\) \(=\frac{a-b+2c}{\frac{3}{2}-\frac{4}{3}+\frac{5}{2}}\)\(=\frac{6}{\frac{8}{3}}=\frac{9}{4}\)
\(\begin{cases}a=\frac{27}{8}\\b=3\\c=\frac{45}{8}\end{cases}\)