\(D=1+3+3^2+3^3+3^4+...+3^{2022}\)

\(3D=3.\left(1+3+3^2+3^3+3^4+...+3^{2022}\right)\)

\(3D=3+3^2+3^3+3^4+3^5+...+3^{2023}\)

\(3D-D=\left(3+3^2+3^3+3^4+3^5+...+3^{2023}\right)-\left(1+3+3^2+3^3+3^4+...+3^{2022}\right)\)

\(2D=\left(3^{2023}-1\right)\)

\(D=\left(3^{2023}-1\right):2\)

3D=3+3^2+...+3^2023

=>2D=3^2023-1

=>\(D=\dfrac{3^{2023}-1}{2}\)

199619 nha

XI

1 more exciting

2 most boring

3 fathest

4 well

5 happier

6 worst

7 colder

8 most difficult

9 better

10 carefully

XII

1 C

2 C

3 B

4 A

5 A

6 B

9 A

10 C

9 B

Câu 4 : 

n H2 = 1,68/22,4 = 0,075(mol)

2R + 2HCl $\to$ 2RCl + H2

n R = 2n H2 = 0,15(mol)

=> M R = 3,45/0,15 = 23(Natri)

Câu 5 : D

6 Drink some water if you are thirsty

7 The children were happy when they saw the Santa Clause

8 He was tired because he had traveled far

9 My brother has given his sister some lovely flowers

10 Where did all the litter come from?

Lời giải:
Theo định lý Viet:

$x_1+x_2=3$

$x_1x_2=m^2$

Khi đó:
$|x_1^2+x_1x_2+3x_2-m^2-2m-1|> 6-m^2$

$\Leftrightarrow |x_1^2+x_1x_2+(x_1+x_2)x_2-m^2-2m-1|> 6-m^2$

$\Leftrightarrow |x_1^2+2x_1x_2+x_2^2-m^2-2m-1|> 6-m^2$
$\Leftrightarrow |(x_1+x_2)^2-m^2-2m-1|> 6-m^2$

$\Leftrightarrow |9-m^2-2m-1|> 6-m^2$

$\Leftrightarrow |m^2+2m-8|> 6-m^2$
Nếu $m^2+2m-8\geq 0$ thì:

$m^2+2m-8> 6-m^2$
$\Leftrightarrow 2m^2+2m-14>0$
$\Leftrightarrow m^2+m-7>0$

$\Leftrightarrow m< \frac{-1-\sqrt{29}}{2}$ hoặc $m> \frac{-1+\sqrt{29}}{2}$

Kết hợp với $m^2+2m-8\geq 0$ suy ra $m\leq -4$ hoặc $m> \frac{-1+\sqrt{29}}{2}$

Nếu $m^2+2m-8<0$ thì:

$-(m^2+2m-8)> 6-m^2$

$\Leftrightarrow m< 1$

Kết hợp với $m^2+2m-8<0$ suy ra $-4< m< 1$

Vậy........