\(=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot2^3\cdot7^3}=\dfrac{2^{12}\cdot3^4\left(3-1\right)}{2^{12}\cdot3^5\left(3-1\right)}-\dfrac{5^{10}\cdot7^3\left(1-7\right)}{5^9\cdot7^3\left(1+2^3\right)}=\dfrac{1}{3}+\dfrac{30}{9}=\dfrac{11}{3}\)

\(M=\left(2x-1\right)\left(2y-1\right)=2xy-2x-2y+1\\ M=2xy-2\left(x+y\right)+1=32-20+1=13\)

\(A=\dfrac{x+7}{\sqrt{x}+3}=\dfrac{x-9+16}{\sqrt{x}+3}=\sqrt{x}-3+\dfrac{16}{\sqrt{x}+3}\\ A=\sqrt{x}+3+\dfrac{16}{\sqrt{x}+3}-6\ge2\sqrt{16}-6=2\\ A_{min}=2\Leftrightarrow\left(\sqrt{x}+3\right)^2=16\Leftrightarrow\sqrt{x}+3=4\left(x\ge0\right)\Leftrightarrow x=1\)

Quãng đường AB dài \(45.3\dfrac{15}{60}=45.3\dfrac{1}{4}=146,25\left(km\right)\)

Đi với 65km/h hết \(146,25:65=2,25\left(h\right)=2h15p\)

Có \(\dfrac{2}{-2}=\dfrac{5}{-5}\ne\dfrac{10}{-12}\) nên hệ vô nghiệm (sách giáo khoa)

\(C=-\left(x^2-4x+4\right)+7=-\left(x-2\right)^2+7\le7\\ C_{max}=7\Leftrightarrow x=2\\ B=-\left(x^2-6x+9\right)-2=-\left(x-3\right)^2-2\le-2\\ B_{max}=-2\Leftrightarrow x=3\)

\(P_2O_3\\ NH_3\\ FeO\\ Cu(OH)_2\\ Ca(NO_3)_2\\ Ag_2SO_4\\ Ba_3(PO_4)_2\\ Fe_2(SO_4)_3\\ Al_2(SO_4)_3\\ NH_4NO_3\)

\(A=\left(x^2-6x+9\right)+2=\left(x-3\right)^2+2\ge2\\ A_{min}=2\Leftrightarrow x=3\\ B=2\left(x^2-10x+25\right)+51=2\left(x-5\right)^2+51\ge51\\ B_{min}=51\Leftrightarrow x=5\\ C=\left[\left(x^2-4xy+4y^2\right)+10\left(x-2y\right)+25\right]+\left(y^2-2y+1\right)+2\\ C=\left(x-2y+5\right)^2+\left(y-1\right)^2+2\ge2\\ C_{min}=2\Leftrightarrow\left\{{}\begin{matrix}x-2y+5=0\\y-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2y-5=2-5=-3\\y=1\end{matrix}\right.\)

\(\left\{{}\begin{matrix}-a+b=6\\2a+b=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3a=-9\\-a+b=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=-3\\b=3\end{matrix}\right.\)

Có \(\dfrac{5}{-5}=\dfrac{1}{-1}=\dfrac{4}{-4}\)

Vậy hệ vô số nghiệm

\(n_{HCl}=\dfrac{50.18,25}{100.36,5}=0,25(mol)\\ K_2CO_3+2HCl\to 2KCl+H_2O+CO_2\uparrow\\ a,n_{CO_2}=0,125(mol)\\ \Rightarrow V_{CO_2}=0,125.22,4=2,8(l)\\ b,n_{K_2CO_3}=0,125(mol)\\ \Rightarrow m_{K_2CO_3}=0,125.138=17,25(g)\\ c,n_{KCl}=0,25(mol)\\ \Rightarrow C\%_{KCl}=\dfrac{0,25.74,5}{17,25+50-0,125.44}.100\%=30,16\%\)