a)

\(\begin{array}{l}2023 - {25^2}:{5^3} + 27\\ = 2023 - {5^4}:{5^3} + 27\\ = 2023 - 5^{4-3} + 27\\ = 2023 -5 + 27\\ =2018+27\\= 2045\end{array}\)

b)

\(\begin{array}{l}60:\left[ {7.\left( {{{11}^2} - 20.6} \right) + 5} \right]\\ = 60:\left[ {7.\left( {121 - 120} \right) + 5} \right]\\ = 60:\left[ {7.1 + 5} \right]\\ = 60:12\\ = 5\end{array}\)

\(B=-4x^2+12x-11\\ =-\left(\left(2x\right)^2-12x+11\right)\\ =-\left(\left(2x\right)^2-2.2x.3+9+2\right)\\ =-\left(2x-3\right)^2-2< 0\)

(vì \(\left(2x-3\right)^2\ge0\forall x\Rightarrow-\left(2x-3\right)^2\le0\forall x\Rightarrow-\left(2x-3\right)^2-2< 0\))

C=-2x^2+2x-5

=-2(x^2-x+5/2)

=-2(x^2-x+1/4+9/4)

=-2(x-1/2)^2-9/2<=-9/2<0 với mọi x

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

Thay x=-2 vào B ta có:
\(B=4x^3+x-2022=4.\left(-2\right)^3+\left(-2\right)-2022=-32-2-2022=-2056\)

Thay x=2 vào B ta có:

\(B=4x^3+x-2022=4.2^3+2-2022=32+2-2022=-1988\)

-1988

a: =>7(x-5)>0

=>x-5>0

=>x>5

b: =>x-1 thuộc {1;-1;11;-11}

=>x thuộc {2;0;12;-10}

c: =>x+1+7 chia hết cho x+1

=>x+1 thuộc {1;-1;7;-7}

=>x thuộc {0;-2;6;-8}

d: =>(x+2)(x-5)<0

=>-2<x<5

a:(- 7) . ( 5 – x) < 0

=>7(x-5)>0

=>x-5>0

=>x>5

b:11 ⁝ x – 1

=>x-1 thuộc {1;-1;11;-11}

=>x thuộc {2;0;12;-10}

c: x + 8 ⁝ x + 1

=>x+1+7 chia hết cho x+1

=>x+1 thuộc {1;-1;7;-7}

=>x thuộc {0;-2;6;-8}

d: (x + 2) . (5 – x) > 0

=>(x+2)(x-5)<0

=>-2<x<5

a) Ta có: \(x^2-x-12=0\)

\(\Leftrightarrow\left(x-4\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-3\end{matrix}\right.\)

b) Ta có: \(x^2+3x-18=0\)

\(\Leftrightarrow\left(x+6\right)\left(x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=3\end{matrix}\right.\)

\(x^2-4x+3=0\\ \Rightarrow\left(x^2-3x\right)-\left(x-3\right)=0\\ \Rightarrow x\left(x-3\right)-\left(x-3\right)=0\\ \Rightarrow\left(x-1\right)\left(x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)

\(x^2-4x+3=0\)

\(\Leftrightarrow x^2-x-3x+3=0\)

\(\Leftrightarrow x\left(x-1\right)-3\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)

\(\Leftrightarrow\left(x-1\right)\left(x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)

\(b,7+3x=3\)

\(\Leftrightarrow3x=-4\)

\(\Leftrightarrow x=-\dfrac{4}{3}\)

\(c,6y+2=20\)

\(\Leftrightarrow6y=18\)

\(\Leftrightarrow y=3\)

\(d,4y=10\)

\(\Leftrightarrow y=\dfrac{10}{4}\)

\(\Leftrightarrow y=\dfrac{5}{2}\)

\(e,5x-7=13\)

\(\Leftrightarrow5x=20\)

\(\Leftrightarrow x=4\)

\(f,\dfrac{4}{3}x+\dfrac{7}{2}=10\)

\(\Leftrightarrow\dfrac{4}{3}x=\dfrac{13}{2}\)

\(\Leftrightarrow x=\dfrac{39}{8}\)

\(g,4-\dfrac{2}{3}y=2\)

\(\Leftrightarrow\dfrac{2}{3}y=2\)

\(\Leftrightarrow y=3\)

\(h,6x=36\Leftrightarrow x=6\)

\(j,7x-3=0\)

\(\Leftrightarrow7x=3\)

\(\Leftrightarrow x=\dfrac{3}{7}\)

`2022 \times 123 \times 12 - 2022 \times 11`

`= 2022 \times (123 \times 12 - 11)`

`= 2022 \times (1476 - 11)`

`= 2022 \times 1465`

`= 2962230`