Toán Lớp 7: Cho a/2009=b/2011=c/2013
CMR: (a-c)2/4=(a-b)(b-c)
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Toán Lớp 7: Cho a/2009=b/2011=c/2013
CMR: (a-c)2/4=(a-b)(b-c)
Nêu cả cách làm hộ mình ạ
Comments ( 1 )
\dfrac{a}{{2009}} = \dfrac{b}{{2011}} = \dfrac{c}{{2013}}\\
= \dfrac{{a – c}}{{2009 – 2013}} = \dfrac{{a – b}}{{2009 – 2011}} = \dfrac{{b – c}}{{2011 – 2013}}\\
= \dfrac{{a – c}}{{ – 4}} = \dfrac{{a – b}}{{ – 2}} = \dfrac{{b – c}}{{ – 2}}\\
\Leftrightarrow \left( {\dfrac{{a – c}}{{ – 4}}} \right).\left( {\dfrac{{a – c}}{{ – 4}}} \right) = \left( {\dfrac{{a – b}}{{ – 2}}} \right).\left( {\dfrac{{b – c}}{{ – 2}}} \right)\\
\Leftrightarrow \dfrac{{{{\left( {a – c} \right)}^2}}}{{16}} = \dfrac{{\left( {a – b} \right).\left( {b – c} \right)}}{4}\\
\Leftrightarrow \dfrac{{{{\left( {a – c} \right)}^2}}}{4} = \left( {a – b} \right).\left( {b – c} \right)\\
Vậy\,\dfrac{{{{\left( {a – c} \right)}^2}}}{4} = \left( {a – b} \right).\left( {b – c} \right)
\end{array}$