B = {3/2;1}

Do phương trình x2 + x + 1 = 0 vô nghiệm nên tập hợp A không có phần tử nào

\(A=\left\{2;9;22\right\}\)

\(B=\left\{-2;1\right\}\)

Đáp án D

Ta có: 2 x 2 − 5 x + 3 = 0 ⇔ x = 1 ∈ ℝ x = 3 2 ∈ ℝ

nên   X = 1 ; 3 2

`#3107.101107`

a,

\(\text{A = }\left\{x\in R\text{ | }\left(2x-x^2\right)\left(3x-2\right)=0\right\}\)

`<=> (2x - x^2)(3x - 2) = 0`

`<=>`\(\left[{}\begin{matrix}2x-x^2=0\\3x-2=0\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x\left(2-x\right)=0\\3x=2\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=0\\2-x=0\\x=\dfrac{2}{3}\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=0\\x=2\\x=\dfrac{2}{3}\end{matrix}\right.\)

Vậy, `A = {0; 2; 2/3}`

b,

\(\text{B = }\left\{x\in R\text{ | }2x^3-3x^2-5x=0\right\}\)

`<=> 2x^3 - 3x^2 - 5x = 0`

`<=> x(2x^2 - 3x - 5) = 0`

`<=>`\(\left[{}\begin{matrix}x=0\\2x^2-3x-5=0\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=0\\2x^2-2x+5x-5=0\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=0\\\left(2x^2-2x\right)+\left(5x-5\right)=0\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=0\\2x\left(x-1\right)+5\left(x-1\right)=0\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=0\\\left(2x+5\right)\left(x-1\right)=0\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=0\\2x+5=0\\x-1=0\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=0\\x=-\dfrac{5}{2}\\x=1\end{matrix}\right.\)

Vậy, `B = {-5/2; 0; 1}.`

c,

\(\text{C = }\left\{x\in Z\text{ | }2x^2-75x-77=0\right\}\)

`<=> 2x^2 - 75x - 77 = 0`

`<=> 2x^2 - 2x + 77x - 77 = 0`

`<=> (2x^2 - 2x) + (77x - 77) = 0`

`<=> 2x(x - 1) + 77(x - 1) = 0`

`<=> (2x + 77)(x - 1) = 0`

`<=>`\(\left[{}\begin{matrix}2x+77=0\\x-1=0\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}2x=-77\\x=1\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=-\dfrac{77}{2}\\x=1\end{matrix}\right.\)

Vậy, `C = {-77/2; 1}`

d,

\(\text{D = }\left\{x\in R\text{ | }\left(x^2-x-2\right)\left(x^2-9\right)=0\right\}\)

`<=> (x^2 - x - 2)(x^2 - 9) = 0`

`<=>`\(\left[{}\begin{matrix}x^2-x-2=0\\x^2-9=0\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x^2+x-2x-2=0\\x^2=9\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}\left(x^2+x\right)-\left(2x+2\right)=0\\x^2=\left(\pm3\right)^2\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x\left(x+1\right)-2\left(x+1\right)=0\\x=\pm3\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}\left(x-2\right)\left(x+1\right)=0\\x=\pm3\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x-2=0\\x+1=0\\x=\pm3\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=2\\x=-1\\x=\pm3\end{matrix}\right.\)

Vậy, `D = {-1; -3; 2; 3}.`

a) \(A = \{ 3;2;1;0; - 1; - 2; - 3; -4; ...\} \)

Tập hợp B là tập các nghiệm nguyên của phương trình \(\left( {5x - 3{x^2}} \right)\left( {{x^2} + 2x - 3} \right) = 0\)

Ta có:

 \(\begin{array}{l}\left( {5x - 3{x^2}} \right)\left( {{x^2} + 2x - 3} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l}5x - 3{x^2} = 0\\{x^2} + 2x - 3 = 0\end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l}\left[ \begin{array}{l}x = 0\\x = \frac{5}{3}\end{array} \right.\\\left[ \begin{array}{l}x = 1\\x =  - 3\end{array} \right.\end{array} \right.\end{array}\)

Vì \(\frac{5}{3} \notin \mathbb Z\) nên \(B = \left\{ { - 3;0;1} \right\}\).

b) \(A \cap B = \left\{ {x \in A|x \in B} \right\} = \{  - 3;0;1\}  = B\)

\(A \cup B = \) {\(x \in A\) hoặc \(x \in B\)} \( = \{ 3;2;1;0; - 1; - 2; - 3;...\}  = A\)

\(A\,{\rm{\backslash }}\,B = \left\{ {x \in A|x \notin B} \right\} = \{ 3;2;1;0; - 1; - 2; - 3;...\} {\rm{\backslash }}\;\{  - 3;0;1\}  = \{ 3;2; - 1; - 2; - 4; - 5; - 6;...\} \)

\(a,C=\left\{0;5;10;15;20;25;30\right\}\\ b,x^2+3x-4=0\\ \Leftrightarrow x^2-x+4x-4=0\\ \Leftrightarrow x\left(x-1\right)+4\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+4\right)=0\\ \Leftrightarrow x-1=0.hoặc.x+4=0\\ \Leftrightarrow x=1.hoặc.x=-4\\ Vậy:D=\left\{-4;1\right\}\)

a) \(2x^3-3x^2-5x=0\)

\(x\left(x+1\right)\left(2x-5\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\left(L\right)\\x=-1\left(TM\right)\\x=\dfrac{5}{2}\left(L\right)\end{matrix}\right.\)

\(A=\left\{-1\right\}\)

b) \(x< \left|3\right|\)\(\Leftrightarrow-3< x< 3\)

\(B=\left\{-2;-1;1;2\right\}\)

c) \(C=\left\{-3;3;6;9\right\}\)

a) \(A=\left\{x\in Z|2x^3-3x^2-5x=0\right\}\)

\(2x^3-3x^2-5x=0\)

\(\Leftrightarrow x\left(2x^2-3x-5\right)=0\)

\(\Leftrightarrow x\left(x+1\right)\left(2x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\\x=\dfrac{5}{2}\left(loại\right)\end{matrix}\right.\)

\(\Rightarrow A=\left\{0;-1\right\}\)

b) \(B=\left\{-2;-1;0;1;2\right\}\)

c) \(C=\left\{-3;3;6;9\right\}\)

a: \(A=\left\{0;1;2;3;4;5\right\}\)

b: \(B=\left\{2;3;4;5\right\}\)

c: \(C=\left\{0;1;-1;2;-2;3;-3\right\}\)