Tìm số tự nhiên a, b, c .d biết : a/b = 5 / 3 ; b/c = 12 / 21 ; c/d = 6 /11 18/08/2021 Bởi Adalyn Tìm số tự nhiên a, b, c .d biết : a/b = 5 / 3 ; b/c = 12 / 21 ; c/d = 6 /11
Đáp án: $\begin{array}{l}\frac{a}{b} = \frac{5}{3} \Rightarrow \frac{a}{5} = \frac{b}{3} \Rightarrow \frac{a}{{20}} = \frac{b}{{12}}\\\frac{b}{c} = \frac{{12}}{{21}} \Rightarrow \frac{b}{{12}} = \frac{c}{{21}}\\ \Rightarrow \frac{a}{{20}} = \frac{b}{{12}} = \frac{c}{{21}} \Rightarrow \frac{a}{{40}} = \frac{b}{{24}} = \frac{c}{{42}}\\\frac{c}{d} = \frac{6}{{11}} \Rightarrow \frac{c}{6} = \frac{d}{{11}} \Rightarrow \frac{c}{{42}} = \frac{d}{{77}}\\ \Rightarrow \frac{a}{{40}} = \frac{b}{{24}} = \frac{c}{{42}} = \frac{d}{{77}} = k\left( {k \ge 0} \right)\\ \Rightarrow \left\{ \begin{array}{l}a = 40k\\b = 24k\\c = 42k\\d = 77k\end{array} \right.\left( {k \ge 0} \right)\end{array}$ Bình luận
Đáp án:
$\begin{array}{l}
\frac{a}{b} = \frac{5}{3} \Rightarrow \frac{a}{5} = \frac{b}{3} \Rightarrow \frac{a}{{20}} = \frac{b}{{12}}\\
\frac{b}{c} = \frac{{12}}{{21}} \Rightarrow \frac{b}{{12}} = \frac{c}{{21}}\\
\Rightarrow \frac{a}{{20}} = \frac{b}{{12}} = \frac{c}{{21}} \Rightarrow \frac{a}{{40}} = \frac{b}{{24}} = \frac{c}{{42}}\\
\frac{c}{d} = \frac{6}{{11}} \Rightarrow \frac{c}{6} = \frac{d}{{11}} \Rightarrow \frac{c}{{42}} = \frac{d}{{77}}\\
\Rightarrow \frac{a}{{40}} = \frac{b}{{24}} = \frac{c}{{42}} = \frac{d}{{77}} = k\left( {k \ge 0} \right)\\
\Rightarrow \left\{ \begin{array}{l}
a = 40k\\
b = 24k\\
c = 42k\\
d = 77k
\end{array} \right.\left( {k \ge 0} \right)
\end{array}$