cho dãy tỉ số bằng nhau a/2019 = b/2021 =c/2023 CMR (a-c)^2 /4 = (a-b) . (b-c) 27/11/2021 Bởi Reese cho dãy tỉ số bằng nhau a/2019 = b/2021 =c/2023 CMR (a-c)^2 /4 = (a-b) . (b-c)
Đáp án: $\begin{array}{l}\dfrac{a}{{2019}} = \dfrac{b}{{2021}} = \dfrac{c}{{2023}} = k\\ \Rightarrow \left\{ \begin{array}{l}a = 2019k\\b = 2021k\\c = 2023k\end{array} \right.\\ \Rightarrow \left\{ \begin{array}{l}a – c = 2019k – 2023k = – 4k\\a – b = 2019k – 2021k = – 2k\\b – c = 2021k – 2023k = – 2k\end{array} \right.\\ \Rightarrow \dfrac{{{{\left( {a – c} \right)}^2}}}{4} = \dfrac{{{{\left( { – 4k} \right)}^2}}}{4} = \dfrac{{16{k^2}}}{4} = 4{k^2}\\\left( {a – b} \right).\left( {b – c} \right) = \left( { – 2k} \right).\left( { – 2k} \right) = 4{k^2}\\ \Rightarrow \dfrac{{{{\left( {a – c} \right)}^2}}}{4} = \left( {a – b} \right).\left( {b – c} \right)\end{array}$ Bình luận
Đáp án:
$\begin{array}{l}
\dfrac{a}{{2019}} = \dfrac{b}{{2021}} = \dfrac{c}{{2023}} = k\\
\Rightarrow \left\{ \begin{array}{l}
a = 2019k\\
b = 2021k\\
c = 2023k
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a – c = 2019k – 2023k = – 4k\\
a – b = 2019k – 2021k = – 2k\\
b – c = 2021k – 2023k = – 2k
\end{array} \right.\\
\Rightarrow \dfrac{{{{\left( {a – c} \right)}^2}}}{4} = \dfrac{{{{\left( { – 4k} \right)}^2}}}{4} = \dfrac{{16{k^2}}}{4} = 4{k^2}\\
\left( {a – b} \right).\left( {b – c} \right) = \left( { – 2k} \right).\left( { – 2k} \right) = 4{k^2}\\
\Rightarrow \dfrac{{{{\left( {a – c} \right)}^2}}}{4} = \left( {a – b} \right).\left( {b – c} \right)
\end{array}$