\(1,\\ 1,A=6\sqrt{2}-5\sqrt{2}-\sqrt{2}+1=1\\ 2,\\ a,P=\dfrac{\sqrt{a}+3+\sqrt{a}-3}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+3\right)}\cdot\dfrac{\sqrt{a}-3}{\sqrt{a}}\\ P=\dfrac{2\sqrt{a}}{\sqrt{a}\left(\sqrt{a}+3\right)}=\dfrac{2}{\sqrt{a}+3}\\ b,P>\dfrac{1}{2}\Leftrightarrow\dfrac{2}{\sqrt{a}+3}-\dfrac{1}{2}>0\Leftrightarrow\dfrac{4-\sqrt{a}+3}{2\left(\sqrt{a}+3\right)}>0\\ \Leftrightarrow\dfrac{7-\sqrt{a}}{\sqrt{a}+3}>0\Leftrightarrow7-\sqrt{a}>0\left(\sqrt{a}+3>0\right)\\ \Leftrightarrow a< 49\)

\(C2,\\ 1,A=2\sqrt{3}+\sqrt{3}-\left(\sqrt{3}-1\right)=2\sqrt{3}+1\\ 2,\\ a,B=\dfrac{\sqrt{x}+1}{\sqrt{x}}\cdot\dfrac{\sqrt{x}-1+\sqrt{x}+1-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ B=\dfrac{2\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}=\dfrac{2}{\sqrt{x}}\\ b,B\in Z\Leftrightarrow\dfrac{2}{\sqrt{x}}\in Z\Leftrightarrow2⋮\sqrt{x}\\ \Leftrightarrow\sqrt{x}\inƯ\left(2\right)=\left\{1;2\right\}\left(\sqrt{x}>0\right)\\ \Leftrightarrow x\in\left\{1;4\right\}\)

\(3,\\ a,A=8\sqrt{3}-12\sqrt{3}+5\sqrt{3}+2\sqrt{3}=3\sqrt{3}\\ b,B=\dfrac{\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}+\dfrac{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}-\sqrt{y}}\\ B=\sqrt{x}-\sqrt{y}+\sqrt{x}+\sqrt{y}=2\sqrt{x}\)

B

Chọn B

`3x^3 -5x^2 +11x-6=0`

`<=>3x^3 -2x^2 -3x^2 + 2x+9x-6=0`

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

`<=>(3x-2)[(x-1/2)^2+11/4]=0`

  Mà `(x-1/2)^2+11/4 > 0`

  `=>3x-2=0`

`<=>x=2/3`

Bài 4

3x³ - 5x² + 11x - 6 = 0

⇔ 3x³ - 2x² - 3x² + 2x + 9x - 6 = 0

⇔ (3x³ - 2x²) - (3x² - 2x) + (9x - 6) = 0

⇔ x²(3x - 2) - x(3x - 2) + 3(3x - 2) = 0

⇔ (3x - 2)(x² - x + 3) = 0

⇔ 3x - 2 = 0 (vì x² - x + 3 > 0 với mọi x)

⇔ 3x = 2

⇔ x = 2/3

Vậy S = {2/3}

Bài 4: 

1: 

a: \(=35x^3-14x^2+7x+14x^2=35x^3+7x\)

b: \(=\dfrac{6x^3-9x^2-10x^2+15x+8x-12}{2x-3}=3x^2-5x+4\)

2: \(\Leftrightarrow\left(2x-1-4x\right)\left(2x-1+4x\right)=0\)

=>(2x+1)(6x-1)=0

=>x=-1/2 hoặc x=1/6

4.

\(A=\left\{1;2;3\right\}\) ; \(B=\left\{0;1;2;3\right\}\) ; \(C=[0;+\infty)\) ; \(D=\left\{\dfrac{1}{2};3\right\}\)

\(\Rightarrow A\subset B\) ; \(A\subset C\); \(B\subset C\) ; \(D\subset C\)

5.

\(A=\left\{\dfrac{1}{2};2\right\}\) ; \(B=\left\{\dfrac{1}{3};2\right\}\)

\(A\cap B=\left\{2\right\}\) ; \(A\cup B=\left\{\dfrac{1}{3};\dfrac{1}{2};2\right\}\)

\(A\backslash B=\left\{\dfrac{1}{2}\right\}\) ; \(B\backslash A=\left\{\dfrac{1}{3}\right\}\)

7.

Các tập con:

\(\varnothing;\left\{a\right\};\left\{b\right\};\left\{c\right\};\left\{d\right\};\left\{a;b\right\};\left\{a;c\right\};\left\{a;d\right\};\left\{b;c\right\};\left\{b;d\right\};\left\{c;d\right\}\)

\(\left\{a;b;c\right\};\left\{a;b;d\right\};\left\{a;c;d\right\};\left\{b;c;d\right\};\left\{a;b;c;d\right\}\)