Question

tìm a,b,c,d biết \(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}=\frac{d}{5}\) và 3a + b - 2c + 4d = 105

Answer 1

Ta có : \(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}=\frac{d}{5}\Leftrightarrow\frac{3a}{6}=\frac{b}{3}=\frac{2c}{8}=\frac{4d}{20}\)

\(\Rightarrow\frac{3a}{6}=\frac{b}{3}=\frac{2c}{8}=\frac{4d}{10}=\frac{3a+b-2c+4d}{6+3-8+}=\frac{105}{21}=5\)

\(\Rightarrow\hept{\begin{cases}\frac{3a}{6}=5\\\frac{b}{3}=5\end{cases}}\Rightarrow\hept{\begin{cases}a=10\\b=15\end{cases}}\)                        \(\Rightarrow\hept{\begin{cases}\frac{2c}{8}=5\\\frac{4d}{20}=5\end{cases}}\Rightarrow\hept{\begin{cases}c=20\\d=25\end{cases}}\)

Answer 2

P/S : 6+3-8+20=21 

Answer 3

\(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}=\frac{d}{5}=\frac{3a}{6}=\frac{b}{3}=\frac{2c}{8}=\frac{4d}{20}\)

\(=\frac{3a+b-2c+4d}{6+3-8+20}=\frac{105}{21}=5\)

Từ đó suy ra a; b; c; d