\(2^{x+3}\cdot4^2=64\\ \Leftrightarrow2^{x+3}\cdot4^2=4^3\\ \Leftrightarrow2^{x+3}=4=2^2\\ \Leftrightarrow x+3=2\Leftrightarrow x=-1\)

\(a,P=\dfrac{x^2+x-x^2+x+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{2}{x-1}\\ b,\left|x-1\right|=2\Leftrightarrow\left[{}\begin{matrix}x-1=2\\1-x=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-1\left(ktm\right)\end{matrix}\right.\\ \Leftrightarrow P=\dfrac{2}{3-1}=1\\ c,P\in Z\Leftrightarrow x-1\inƯ\left(2\right)=\left\{-2;-1;1;2\right\}\\ \Leftrightarrow x\in\left\{0;2;3\right\}\left(x\ne-1\right)\)

Chiều cao CE là \(3\times2=6\left(cm\right)\)

Cạnh lớn của hbh là \(24:3=8\left(cm\right)\)

Cạnh nhỏ của hbh là \(24:6=4\left(cm\right)\)

Chu vi hbh là \(\left(8+4\right)\times2=24\left(cm\right)\)

\(a,2^{150}=\left(2^3\right)^{50}=8^{50}< 9^{50}=\left(3^2\right)^{50}=3^{100}\\ b,2^{24}=\left(2^3\right)^8=8^8< 9^8=\left(3^2\right)^8=3^{16}\)

\(12=2^2.3\\ 21=3.7\\ \Rightarrow BCNN\left(12,21\right)=2^2.3.7=84\\ \Rightarrow x\in BC\left(12,21\right)=B\left(84\right)=\left\{0;84;168;252;...\right\}\\ \text{Mà }100< x< 200\Rightarrow x=168\)

\(\Leftrightarrow\left|2x-1\right|=\dfrac{1}{3}+\dfrac{1}{2}=\dfrac{5}{6}\\ \Leftrightarrow\left[{}\begin{matrix}2x-1=\dfrac{5}{6}\\1-2x=\dfrac{5}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{11}{6}\\2x=\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{11}{12}\\x=\dfrac{1}{12}\end{matrix}\right.\)

\(\dfrac{x}{2}=\dfrac{y}{5}\Leftrightarrow\dfrac{x^2}{4}=\dfrac{y^2}{25}=\dfrac{10x^2-y^2}{10\cdot4-25}=\dfrac{x^2+y^2}{4+25}\\ \Leftrightarrow A=\dfrac{40-25}{29}=\dfrac{15}{29}\)

\(ĐK:x\ge1\\ PT\Leftrightarrow\sqrt{x+4}=2-\sqrt{x-1}\\ \Leftrightarrow x+4=x+3-4\sqrt{x-1}\\ \Leftrightarrow4\sqrt{x-1}=-1\Leftrightarrow x\in\varnothing\)

Vậy \(S\in\varnothing\)

\(\cos^4\alpha-\sin^4\alpha+1\\ =\left(\sin^2\alpha+\cos^2\alpha\right)\left(-\sin^2\alpha+\cos^2\alpha\right)+\left(\sin^2\alpha+\cos^2\alpha\right)\\ =-\sin^2\alpha+\cos^2\alpha+\sin^2\alpha+\cos^2\alpha=2\cos^2\alpha\)