\(3,\\ A=\dfrac{1}{x^2-4x+9}=\dfrac{1}{\left(x-2\right)^2+5}\)

Vì \(\left(x-2\right)^2+5\ge5\Leftrightarrow A\le\dfrac{1}{5}\)

\(A_{max}=\dfrac{1}{5}\Leftrightarrow x=2\)

\(B=\dfrac{1}{x^2-6x+17}=\dfrac{1}{\left(x-3\right)^2+8}\)

Vì \(\left(x-3\right)^2+8\ge8\Leftrightarrow B\le\dfrac{1}{8}\)

\(B_{max}=\dfrac{1}{8}\Leftrightarrow x=3\)

Bài 5: 

a: Xét ΔBEC và ΔADC có 

\(\widehat{C}\) chung

\(\widehat{EBC}=\widehat{DAC}\)

Do đó: ΔBEC\(\sim\)ΔADC

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 \(\Delta ADH=\Delta BCK\left(ch-gn\right)\)

\(\Rightarrow DH=CK\)

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) \(n_{FeCl2}=\dfrac{0,1.1}{1}=0,1\left(mol\right)\)

⇒ \(m_{FeCl2}=0,1.127=12,7\left(g\right)\)

 Chúc bạn học tốt

Bài 7:

a: \(A=x+\sqrt{x}\ge0\forall x\)

Dấu '=' xảy ra khi x=0

\(4,\\ b,B=\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}\ge3\sqrt[3]{\dfrac{xyz}{xyz}}=3\)

Dấu \("="\Leftrightarrow x=y=z\)

\(c,x+y=4\Leftrightarrow x=4-y\\ \Leftrightarrow C=\left(4-y\right)^2+y^2\\ C=16-8y+y^2+y^2=2\left(y^2-4y+4\right)+8\\ C=2\left(y-2\right)^2+8\ge8\\ C_{min}=8\Leftrightarrow x=y=2\)