Mn giúp em vs ạ
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Gọi O là trung điểm IK \(\Rightarrow OI=OK=\dfrac{1}{2}IK\)
\(\left(\overrightarrow{MI}+\overrightarrow{IA}\right)\left(\overrightarrow{MI}+\overrightarrow{IB}\right)+\left(\overrightarrow{MK}+\overrightarrow{KC}\right)\left(\overrightarrow{MK}+\overrightarrow{KD}\right)=\dfrac{1}{2}Ik^2\)
\(\Leftrightarrow MI^2-IA^2+MK^2-KC^2=\dfrac{1}{2}IK^2\)
\(\Leftrightarrow\left(\overrightarrow{MO}+\overrightarrow{OI}\right)^2+\left(\overrightarrow{MO}+\overrightarrow{OK}\right)^2=IA^2+KC^2+\dfrac{1}{2}IK^2\)
\(\Leftrightarrow2MO^2+2OI^2=IA^2+KC^2+\dfrac{1}{2}IK^2\)
\(\Leftrightarrow2MO^2+\dfrac{1}{2}IK^2=IA^2+KC^2+\dfrac{1}{2}IK^2\)
\(\Leftrightarrow MO^2=\dfrac{1}{2}\left(IA^2+KC^2\right)=\dfrac{1}{8}\left(AB^2+CD^2\right)\)
\(\Leftrightarrow MO=\dfrac{1}{2\sqrt{2}}\sqrt{AB^2+CD^2}\)
Tập hợp M là đường tròn tâm O bán kính \(\dfrac{\sqrt{AB^2+CD^2}}{2\sqrt{2}}\)
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\(CuO\) + \(H_2\)→ \(Cu\) + \(H_2O\)
\(O_2\) + \(2H_2\) → \(2H_2O\)
\(PbO\) + \(H_2\) → \(H_2O\) + \(Pb\)
\(Fe_2O_3\) + \(3H_2\) → \(2Fe\) + \(3H_2O\)
\(Fe_3O_4\) + \(4H_2\) → \(3Fe\) + \(4H_2O\)
\(HgO\) + \(H_2\) → \(Hg\) + \(H_2O\)
a) \(-\dfrac{1}{6}+\dfrac{5}{13}-\dfrac{5}{13}-\dfrac{11}{12}=-\dfrac{1}{6}-\dfrac{11}{12}=-\dfrac{13}{12}\)
b) \(\dfrac{3^4\cdot4-3^6}{3^5\cdot5+10\cdot3^6}=\dfrac{3^4\left(4-3^2\right)}{3^4\left(15+10\cdot3^2\right)}=\dfrac{4-9}{15+90}=-\dfrac{1}{21}\)
c) \(\left(1-\dfrac{3}{4}\right)^2+\left|-\dfrac{4}{5}\right|-\dfrac{29}{80}\cdot2019^2\) (Câu này thì bạn bấm máy cho nhanh :))