\(=2^3.\left(19-14\right)+1=2^3.5+1=8.5+1=40+1=41\)

\(=8\left(19-14\right)+1=8.5+1=41\)

=41

Lời giải:
PT $\Leftrightarrow (\frac{x+1}{2022}+1)+(\frac{x+2}{2021}+1)+...+(\frac{x+23}{2000}+1)=0$

$\Leftrightarrow \frac{x+2023}{2022}+\frac{x+2023}{2021}+...+\frac{x+2023}{2000}=0$

$\Leftrightarrow (x+2023)(\frac{1}{2022}+\frac{1}{2021}+...+\frac{1}{2000})=0$
Dễ thấy tổng trong () luôn dương 

$\Rightarrow x+2023=0$

$\Leftrightarrow x=-2023$

\(\left|2x-3\right|=3-2x\)

\(ĐK:x\le\dfrac{3}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3=3-2x\\3-2x=3-2x\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\0=0\left(đúng\right)\end{matrix}\right.\)

Vậy \(S=\left\{x\in R;x=\dfrac{3}{2}\right\}\)

x - 320 : 32 = 25 . 16

x - 10 = 400

x = 400 + 10

x = 410

\(=>x=\left(320:32\right)+\left(25.26\right)=10+400=410\)

\(x-10=400\)

\(x=400+10\)

\(x=410\)

\(=15\left(23+45+32\right)=15\cdot100=1500\)

=15 x (23+45+32)

=15 x 100

=1500

\(3x\left(x-y\right)+x-y\)

\(=3x\left(x-y\right)+1\left(x-y\right)\)

\(=\left(x-y\right)\left(3x+1\right)\)

\(=\left(x-y\right)\left(3x+1\right)\)

=>8(x+1/x)^2+4[(x+1/x)^2-2]^2-4[(x+1/x)^2-2](x+1/x)^2=(x+4)^2

Đặt x+1/x=a(a>=2)

=>8a^2+4[a^2-2]^2-4[a^2-2]*a^2=(x+4)^2

=>8a^2+4a^4-16a^2+16-4a^4+8a^2=(x+4)^2

=>(x+4)^2=16

=>x+4=4 hoặc x+4=-4

=>x=-8;x=0

Điều kiện: \(x\ne0\)

\(\Leftrightarrow8\left(x+\dfrac{1}{x}\right)^2+4\left(x^2+\dfrac{1}{x^2}\right)\left[\left(x^2+\dfrac{1}{x^2}\right)-\left(x+\dfrac{1}{x}\right)^2\right]=\left(x+4\right)^2\)

\(\Leftrightarrow8\left(x+\dfrac{1}{x}\right)^2-8\left(x^2+\dfrac{1}{x^2}\right)=\left(x+4\right)^2\\ \Leftrightarrow\left(x+4\right)^2=16\\ \Rightarrow\left\{{}\begin{matrix}x=0\\x=-8\end{matrix}\right.\)

Vì \(x\ne0\) nên \(S=\left\{-8\right\}\)

\(\left(2^3\cdot9^4+9^3+45\right):\left(9^2\cdot10-9^2\right)\)

\(=\dfrac{9^3\cdot\left(2^3\cdot9+1\right)+45}{9^3}\)

\(=\dfrac{9^3\cdot73+45}{9^3}=\dfrac{5918}{81}\)

\(=\dfrac{32}{15}\cdot\dfrac{9}{17}\cdot\dfrac{3}{32}\cdot\dfrac{-17}{3}=-\dfrac{9}{3}=-3\)

=(22/15.3/32)   .   (9/17  :  -3/17)

=66/480     .     (-3)

=11/80  . (-3)

=-33/80

\(\left(2\dfrac{2}{15}\cdot\dfrac{9}{17}\cdot\dfrac{3}{32}\right):\left(-\dfrac{3}{17}\right)\)

\(=\left(\dfrac{32}{15}\cdot\dfrac{9}{17}\cdot\dfrac{3}{32}\right):\left(-\dfrac{3}{17}\right)\)

\(=\dfrac{9}{85}:\left(-\dfrac{3}{17}\right)\)

\(=\dfrac{9}{85}\cdot-\dfrac{17}{3}\)

\(=-\dfrac{3}{5}\)