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Bài 5:
a: Xét ΔBEC và ΔADC có
\(\widehat{C}\) chung
\(\widehat{EBC}=\widehat{DAC}\)
Do đó: ΔBEC\(\sim\)ΔADC
Bài 2:
Thay x=3 và y=-5 vào (d), ta được:
b-6=-5
hay b=1
Bài 7:
a: \(A=x+\sqrt{x}\ge0\forall x\)
Dấu '=' xảy ra khi x=0
a) ĐKXĐ: \(\left\{{}\begin{matrix}x\le-1\\x\ge2\end{matrix}\right.\)
\(\sqrt{x^2-x-2}-\sqrt{x-2}=0\\ \Leftrightarrow\sqrt{x^2-x-2}=\sqrt{x-2}\\ \Leftrightarrow x^2-x-2=x-2\\ \Leftrightarrow x^2-2x=0\\ \Leftrightarrow x\left(x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=2\left(tm\right)\end{matrix}\right.\)
\(a,ĐK:x\ge2\\ PT\Leftrightarrow x^2-x-2=x-2\\ \Leftrightarrow x^2-2x=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\x=0\left(ktm\right)\end{matrix}\right.\Leftrightarrow x=2\\ b,ĐK:\left[{}\begin{matrix}x\le-1\\x\ge1\end{matrix}\right.\\ PT\Leftrightarrow\sqrt{x^2-1}=x^2-1\\ \Leftrightarrow x^2-1=\left(x^2-1\right)^2\\ \Leftrightarrow\left(x^2-1\right)\left(x^2-1-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\left(tm\right)\\x=-1\left(tm\right)\\x=\sqrt{2}\left(tm\right)\\x=-\sqrt{2}\left(tm\right)\end{matrix}\right.\)
\(c,ĐK:\left[{}\begin{matrix}x\le-2\\x\ge1\end{matrix}\right.\\ PT\Leftrightarrow\sqrt{x^2-x}=-\sqrt{x^2+x-2}\\ \Leftrightarrow x^2-x=x^2+x-2\\ \Leftrightarrow2x=2\\ \Leftrightarrow x=1\left(tm\right)\)
\(4,\\ b,B=\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}\ge3\sqrt[3]{\dfrac{xyz}{xyz}}=3\)
Dấu \("="\Leftrightarrow x=y=z\)
\(c,x+y=4\Leftrightarrow x=4-y\\ \Leftrightarrow C=\left(4-y\right)^2+y^2\\ C=16-8y+y^2+y^2=2\left(y^2-4y+4\right)+8\\ C=2\left(y-2\right)^2+8\ge8\\ C_{min}=8\Leftrightarrow x=y=2\)
a, Xét tg ADH và tg BCK có
\(AD=BC;\widehat{ADH}=\widehat{BCK}\) (hình thang cân ABCD)\(;\widehat{AHD}=\widehat{BKC}\left(=90^0\right)\)
Nên \(\Delta ADH=\Delta BCK\left(ch-gn\right)\)
\(\Rightarrow DH=CK\)
\(a,x+\dfrac{1}{2}=\dfrac{3}{4}\\ x=\dfrac{3}{4}-\dfrac{1}{2}\\ x=\dfrac{1}{2}\\ b,-\dfrac{2}{3}-x=1\\x=-\dfrac{2}{3}-1\\ x=-\dfrac{5}{3}\\ d,\dfrac{1}{4}+\dfrac{3}{4}:x=\dfrac{5}{2}\\ \dfrac{3}{4}:x=\dfrac{5}{2}-\dfrac{1}{4}\\ \dfrac{3}{4}:x=\dfrac{9}{4}\\ x=\dfrac{3}{4}:\dfrac{9}{4}\\ x=\dfrac{1}{3}\\ e,\left(x+\dfrac{1}{4}\right)\cdot\dfrac{3}{4}=-\dfrac{5}{8}\\ x+\dfrac{1}{4}=-\dfrac{5}{8}:\dfrac{3}{4}\\ x+\dfrac{1}{4}=\dfrac{5}{6}\\ x=\dfrac{5}{6}-\dfrac{1}{4}\\ x=\dfrac{7}{12}\)
\(g,\dfrac{x-3}{15}=\dfrac{-2}{5}\\ 5\left(x-3\right)=-30\\ x-3=-6\\ x=-6+3\\ x=-3\\ h,\dfrac{x}{-2}=\dfrac{-8}{x}\\ x^2=16\\ x=\pm\sqrt{16}\\ x=\pm4\\ k,\dfrac{x+2}{3}=\dfrac{x-4}{5}\\ 5\left(x+2\right)=3\left(x-4\right)\\ 5x+10=3x-12\\ 5x-3x=-12-10\\ 2x=-22\\ x=-11\)
\(m,\left(2x-1\right)^2=4\\ \Rightarrow\left[{}\begin{matrix}2x-1=2\\2x-1=-2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=3\\2x=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
Bài 6 :
\(n_{Fe}=\dfrac{5,6}{56}=0,1\left(mol\right)\)
Pt : \(Fe+2HCl\rightarrow FeCl_2+H_2|\)
1 2 1 1
0,1 0,1 0,1
a) \(n_{H2}=\dfrac{0,1.1}{1}=0,1\left(mol\right)\)
\(V_{H2\left(dktc\right)}=0,1.22,4=2,24\left(l\right)\)
b) \(n_{FeCl2}=\dfrac{0,1.1}{1}=0,1\left(mol\right)\)
⇒ \(m_{FeCl2}=0,1.127=12,7\left(g\right)\)
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