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DD
27 tháng 9 2021

5. \(10x^2+24xy-28x+16y^2-24y+41\)

\(=x^2-10x+25+9x^2+16y^2+9+24xy-18x-24y+7\)

\(=\left(x-5\right)^2+\left(3x+4y-3\right)^2+7\ge7\)

Dấu \(=\)khi \(\hept{\begin{cases}x-5=0\\3x+4y-3=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=5\\y=-3\end{cases}}\)

5 tháng 12 2021

\(a,ĐK:x+y\ne0;x\ne y\\ HPT\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2}{x+y}+\dfrac{4}{x-y}=\dfrac{14}{3}\left(1\right)\\\dfrac{3}{x+y}+\dfrac{4}{x-y}=5\left(2\right)\end{matrix}\right.\\ \left(2\right)-\left(1\right)=\dfrac{1}{x+y}=\dfrac{1}{3}\\ \Leftrightarrow x+y=3\\ \Leftrightarrow x=3-y\\ \text{Thay vào }\left(1\right)\Leftrightarrow\dfrac{2}{3}+\dfrac{4}{3-2y}=\dfrac{14}{3}\\ \Leftrightarrow\dfrac{4}{3-2y}=4\\ \Leftrightarrow3-2y=1\\ \Leftrightarrow y=1\Leftrightarrow x=2\)

Vậy hệ có nghiệm \(\left(x;y\right)=\left(2;1\right)\)

5 tháng 12 2021

\(b,ĐK:y\ne-\dfrac{1}{2};x-2y\ne0\\ HPT\Leftrightarrow\left\{{}\begin{matrix}\dfrac{6}{x-2y}+\dfrac{y}{1+2y}=3\left(1\right)\\\dfrac{6}{x-2y}-\dfrac{8}{1+2y}=-2\left(2\right)\end{matrix}\right.\\ \left(1\right)-\left(2\right)=\dfrac{y+8}{2y+1}=5\\ \Leftrightarrow y+8=10y+5\Leftrightarrow y=\dfrac{1}{3}\\ \text{Thay vào }\left(1\right)\Leftrightarrow\dfrac{6}{x-\dfrac{2}{3}}+\dfrac{\dfrac{1}{3}}{\dfrac{5}{3}}=3\\ \Leftrightarrow\dfrac{6}{x-\dfrac{2}{3}}=\dfrac{14}{5}\\ \Leftrightarrow x-\dfrac{2}{3}=\dfrac{15}{7}\Leftrightarrow x=\dfrac{59}{21}\)

Vậy hệ có nghiệm \(\left(x;y\right)=\left(\dfrac{59}{21};\dfrac{1}{3}\right)\)

7 tháng 12 2021

\(12,ĐK:x,y\ne0\\ HPT\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4}{x}+\dfrac{2}{y}=4\\\dfrac{6}{x}-\dfrac{2}{y}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{10}{x}=5\\\dfrac{2}{x}+\dfrac{1}{y}=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\\dfrac{1}{y}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\left(tm\right)\)

\(13,\Leftrightarrow\left\{{}\begin{matrix}3\left(x+1\right)+2\left(x+2y\right)=4\\8\left(x+1\right)-2\left(x+2y\right)=18\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}11\left(x+1\right)=22\\3\left(x+1\right)+2\left(x+2y\right)=4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=1\\6+2+4y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\)

\(14,ĐK:x+y\ne0;y\ne1\\ HPT\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4}{x+y}+\dfrac{1}{y-1}=5\\\dfrac{4}{x+y}-\dfrac{8}{y-1}=-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x+y}-\dfrac{2}{y-1}=-1\\\dfrac{9}{y-1}=9\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x+2}=1\\y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+2=1\\y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1\\y=2\end{matrix}\right.\left(tm\right)\)

\(15,ĐK:x\ge-1\\ HPT\Leftrightarrow\left\{{}\begin{matrix}2\left(x+y\right)+\sqrt{x+1}=4\\2\left(x+y\right)-6\sqrt{x+1}=-10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7\sqrt{x+1}=14\\2\left(x+y\right)+\sqrt{x+1}=4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=3\left(tm\right)\\6+2y+2=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-2\end{matrix}\right.\left(tm\right)\)

7 tháng 12 2021

\(16,ĐK:x\ne1;y\ne-2\\ HPT\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3x}{x-1}-\dfrac{2}{y+2}=4\\\dfrac{4x}{x-1}+\dfrac{2}{y+2}=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{7x}{x-1}=14\\\dfrac{2x}{x-1}+\dfrac{1}{y+2}=5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=2\\\dfrac{1}{y+2}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=-1\end{matrix}\right.\left(tm\right)\)

\(17,ĐK:x\ge0;y\ge1\\ HPT\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x}+2\sqrt{y-1}=5\\8\sqrt{x}-2\sqrt{y-1}=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9\sqrt{x}=9\\\sqrt{x}+2\sqrt{y-1}=5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=1\\\sqrt{y-1}=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=5\end{matrix}\right.\)

\(18,\Leftrightarrow\left\{{}\begin{matrix}8x-2\left|y+2\right|=6\\x+2\left|y+2\right|=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x=9\\x+2\left|y+2\right|=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=1\\\left|y+2\right|=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\\left[{}\begin{matrix}y=-1\\y=-3\end{matrix}\right.\end{matrix}\right.\\ 20,ĐK:y\ne1\\ HPT\Leftrightarrow\left\{{}\begin{matrix}2x+\dfrac{3}{y-1}=5\\12x-\dfrac{3}{y-1}=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}14x=14\\2x+\dfrac{3}{y-1}=5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=1\\\dfrac{3}{y-1}=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2\end{matrix}\right.\left(tm\right)\)

\(21,ĐK:x\ne-1\\ HPT\Leftrightarrow\left\{{}\begin{matrix}\dfrac{9}{x+1}-6y=-3\\\dfrac{10}{x+1}+6y=22\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{19}{x+1}=19\\\dfrac{3}{x+1}-2y=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\3-2y=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=2\end{matrix}\right.\left(tm\right)\)

27 tháng 10 2021

Câu 6

Thay x=-1 và y=2 vào (d), ta được:

-m+1+2m-3=2

\(\Leftrightarrow m=4\)

27 tháng 10 2021

Câu 5:

Gọi đths cần tìm là \(y=ax+b\left(a\ne0\right)\)

Vì đt vuông góc với \(y=2x+7\) nên \(2a=-1\Leftrightarrow a=-\dfrac{1}{2}\)

 

Do đó hệ số góc của đt là \(a=-\dfrac{1}{2}\)

27 tháng 10 2021

a: Thay \(x=9+4\sqrt{2}\) vào A, ta được:

\(A=\dfrac{2\sqrt{2}+1+7}{2\sqrt{2}+1-1}=\dfrac{8+2\sqrt{2}}{2\sqrt{2}}=2\sqrt{2}+1\)

25 tháng 10 2023

Câu 7:

a, \(Fe+H_2SO_4\rightarrow FeSO_4+H_2\)

\(CuO+H_2SO_4\rightarrow CuSO_4+H_2O\)

b, \(n_{H_2}=\dfrac{2,24}{22,4}=0,1\left(mol\right)\)

Theo PT: \(n_{Fe}=n_{H_2}=0,1\left(mol\right)\)

\(\Rightarrow\left\{{}\begin{matrix}\%m_{Fe}=\dfrac{0,1.56}{10}.100\%=56\%\\\%m_{CuO}=44\%\end{matrix}\right.\)

c, \(n_{CuO}=\dfrac{10-0,1.56}{80}=0,055\left(mol\right)\)

Theo PT: \(n_{H_2SO_4}=n_{Fe}+n_{CuO}=0,155\left(mol\right)\)

\(\Rightarrow C\%_{H_2SO_4}=\dfrac{0,155.98}{100}.100\%=15,19\%\)

d, Theo PT: \(\left\{{}\begin{matrix}n_{FeSO_4}=n_{Fe}=0,1\left(mol\right)\\n_{CuSO_4}=n_{CuO}=0,055\left(mol\right)\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}m_{FeSO_4}=0,1.152=15,2\left(g\right)\\m_{CuSO_4}=0,055.160=8,8\left(g\right)\end{matrix}\right.\)

25 tháng 10 2023

Câu 8:

a, \(CuCO_3+2HCl\rightarrow CuCl_2+CO_2+H_2O\)

b, \(n_{CO_2}=\dfrac{3,36}{22,4}=0,15\left(mol\right)\)

Theo PT: \(n_{CuCO_3}=n_{CO_2}=0,15\left(mol\right)\)

\(\Rightarrow\left\{{}\begin{matrix}\%m_{CuCO_3}=\dfrac{0,15.124}{20}.100\%=93\%\\\%m_{CuCl_2}=7\%\end{matrix}\right.\)

c, \(n_{HCl}=2n_{CO_2}=0,3\left(mol\right)\)

\(\Rightarrow C_{M_{HCl}}=\dfrac{0,3}{0,2}=1,5\left(M\right)\)

27 tháng 10 2021

Câu 3: 
Thay x=-1 và y=0 vào (d), ta được:

-m+2m-1=0

hay m=1