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1, \(x^4-19x^2-10x+8=0\)
\(\Leftrightarrow\left(x+4\right)\left(x^3-4x^2-3x+2\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x+1\right)\left(x^2-5x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+1=0\\x^2-5x+2=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x_1=-4\\x_2=-1\end{matrix}\right.\)
hoặc \(x^2-5x+2=0\)
\(\Rightarrow\Delta=17\left(CT:b^2-4ac\right)\)
\(\Rightarrow\left[{}\begin{matrix}x_3=\dfrac{5+\sqrt{17}}{2}\\x_4=\dfrac{5-\sqrt{17}}{2}\end{matrix}\right.\)
Vậy pt có 4 no là...........
\(\left|\dfrac{1}{2}x\right|=3-2x\)(1)
Vì \(VT\ge0\Rightarrow3-2x\ge0\Leftrightarrow x\le\dfrac{3}{2}\)
\(\left(1\right)\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x=3-2x\\\dfrac{1}{2}x=-3+2x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{6}{5}\left(Chon\right)\\x=2\left(Loai\right)\end{matrix}\right.\)
Vậy....
\(\overrightarrow{AB}=3\overrightarrow{AM};\overrightarrow{CD}=2\overrightarrow{CN};\overrightarrow{BI}=\frac{6}{11}\overrightarrow{BC}\)
Có tứ giác ABCD là hbh=> \(\overrightarrow{CD}=\overrightarrow{BA}\Rightarrow\overrightarrow{BA}=2\overrightarrow{CN}\)
Có G là trọng tâm tam giác BMN
\(\Rightarrow\overrightarrow{GB}+\overrightarrow{GM}+\overrightarrow{GN}=\overrightarrow{0}\)
\(\Leftrightarrow3\overrightarrow{GA}+\overrightarrow{AB}+\overrightarrow{AN}+\overrightarrow{AM}=\overrightarrow{0}\)\(\Leftrightarrow3\overrightarrow{GA}+\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{CN}+\frac{1}{3}\overrightarrow{AB}=\overrightarrow{0}\)
\(\Leftrightarrow3\overrightarrow{GA}+\frac{4}{3}\overrightarrow{AB}+\frac{1}{2}\overrightarrow{BA}+\overrightarrow{AB}+\overrightarrow{AD}=\overrightarrow{0}\)
\(\Leftrightarrow3\overrightarrow{AG}=\frac{-11}{6}\overrightarrow{AB}-\overrightarrow{AD}\Leftrightarrow\overrightarrow{AG}=\frac{-11}{18}\overrightarrow{AB}-\frac{1}{3}\overrightarrow{AD}\)
Có \(\overrightarrow{AN}=\overrightarrow{AC}+\overrightarrow{CN}=\frac{1}{2}\overrightarrow{BA}+\overrightarrow{AB}+\overrightarrow{AD}=\frac{1}{2}\overrightarrow{AB}+\overrightarrow{AD}\)
b/ \(\overrightarrow{AG}=\frac{-11}{18}\overrightarrow{AB}-\frac{1}{3}\overrightarrow{AD}\)
\(\overrightarrow{AI}=\overrightarrow{AB}+\overrightarrow{BI}=\overrightarrow{AB}+\frac{6}{11}\overrightarrow{BC}=\overrightarrow{AB}+\frac{6}{11}\overrightarrow{AD}\)
Có \(\overrightarrow{AG}=-\frac{11}{18}\overrightarrow{AI}\Rightarrow\) thẳng hàng
Tính AG còn sai, mà AG=-AI vẫn bảo thẳng hàng. Không biết làm thì đừng thể hiện
Câu 2 :
b) \(\frac{x}{3}=\frac{-2}{9}\)
=> x = \(\frac{-2}{9}.3\) = \(\frac{-2}{3}\)
c) \(0,5x-\frac{2}{3}x=\frac{7}{12}\)
=> \(\frac{1}{2}x-\frac{2}{3}x=\frac{7}{12}\)
=> \(-\frac{1}{6}\)x = \(\frac{7}{12}\)
=> x = \(\frac{7}{12}:\frac{-1}{6}\)
=> x =\(\frac{-7}{2}\)
Đề 1 câu 5 :
\(3B=3^2+3^3+3^4+...+3^{201}\)
\(\Rightarrow2B=3B-B=3^{201}-3\)
\(\Rightarrow2B+3=\left(3^{201}-3\right)+3=3^{201}\)
Do đó n = 201
vt MA + vt MB + vt MC = 3 vt MG
Xét VT = (đề bài VT ) = vt MG + vt GA + vt MG + vt GB + vt MG + vt GC = 3 vt MG + ( vt GA + GB + GC ) = 3 vt MG = VP
( G là trọng tâm nên ( vt GA + GB + GC ) = 0 )