\(\dfrac{2022\times2023-1}{2023\times2021+2022}\)

= \(\dfrac{\left(2021+1\right)\times2023-1}{2023\times2021+2022}\)

= \(\dfrac{2023\times2021+2023-1}{2023\times2021+2022}\)

= \(\dfrac{2023\times2021+2022}{2023\times2021+2022}\)

= 1

2023×2021+20222022×2023−1​

= (2021+1)×2023−12023×2021+20222023×2021+2022(2021+1)×2023−1​

= 2023×2021+2023−12023×2021+20222023×2021+20222023×2021+2023−1​

= 2023×2021+20222023×2021+20222023×2021+20222023×2021+2022​

= 1

cảm ơn nhưng bạn trình bày chi tiết hộ mk đc ko

Sửa đề: \(\frac{2022\times2023-3}{2023\times2021+2020}\)

\(=\frac{2023\times2021+2023-3}{2023\times2021+2020}\)

\(=\frac{2023\times2021+2020}{2023\times2021+2020}\)

=1

\(2022\times2005-2000\times2022+15\times2022-20\times2021\)

\(=2022\times\left(2005-2000+15\right)-20\times2021\)

\(=2022\times20-20\times2021\)

\(=20\times\left(2022-2021\right)\)

\(=20\times1\)

\(=20\)

a, 2022 \(\times\) 2005 - 2000 \(\times\) 2022 + 15 \(\times\) 2022 - 20 \(\times\) 2021

= (2022  \(\times\) 2005 - 2000 \(\times\) 2022 + 15 \(\times\) 2022 )- 20 \(\times\) 2021

= 2022 \(\times\) (2005 - 2000 + 15) - 20  \(\times\) 2021

= 2022 \(\times\) (5 +15)  - 20 \(\times\) 2021

= 2022 \(\times\) 20 - 20 \(\times\) 2021

= 20 \(\times\) (2022 - 2021)

= 20 \(\times\) 1

= 20 

   \(\dfrac{2021}{2022}\) x \(\dfrac{2022020222022}{202320232023}\) x \(\dfrac{20212021}{20232023}\)

= \(\dfrac{2021}{2022}\) x \(\dfrac{2022}{2023}\) x \(\dfrac{2021}{2023}\)

= \(\dfrac{2021\times2021}{2023\times2023}\)

= \(\dfrac{4084441}{4092529}\)

help me !!!!!!!

\(=2021\cdot2\cdot\left(1+\dfrac{1}{2}:\dfrac{3}{2}-\dfrac{4}{3}\right)=4042\cdot\left(1+\dfrac{1}{3}-\dfrac{4}{3}\right)=0\)

Tính chậm đc ko :v

đề bài là tính nhanh mà

-13.21-13.80+13

=-13.(21-80+1)

=-13.100

=-1300

-1+2-3+4-5+6-...-2021+2022

=(-1+2)+(-3+4)+...+(-2021+2022)

=1+1+1+...+1 (1011 số hạng)
=1011

-13 . 21 - 13 . 80 + 13

13 ( -21 - 80 + 1 )

13 . ( -100 )

- 1300

Đây nhé bé

Câu1

Vì \(\mid x \mid \geq 0 \Rightarrow \mid x \mid + 1 \geq 1\).
Do đó \(\left(\right. \mid x \mid + 1 \left.\right)^{10} \geq 1^{10} = 1\).

Suy ra:

\(A = \left(\right. \mid x \mid + 1 \left.\right)^{10} + 2023 \geq 1 + 2023 = 2024.\)

Dấu “=” chỉ xảy ra khi \(\mid x \mid = 0 \Leftrightarrow x = 0\).

\(\Rightarrow\) Giá trị nhỏ nhất của \(A\) là \(\boxed{2024}\), đạt tại \(x = 0\).

Câu 2 ( câu này kiến thức nâng cao nhé em nên là khi em đọc lời giải sẽ có khó hiểu nhé )

Đặt \(n = 2022\). Khi đó:

\(A = \frac{n^{2022} + 1}{n^{2023} + 1} , B = \frac{n^{2021} + 1}{n^{2022} + 1} .\)

Xét tổng quát với \(a_{k} = \frac{n^{k} + 1}{n^{k + 1} + 1} , \left(\right. n > 1 \left.\right)\).

Ta gọi k là luỹ thừa của cơ số

\(a_{k} > a_{k - 1} \textrm{ }\textrm{ } \Longleftrightarrow \textrm{ }\textrm{ } \left(\right. n^{k} + 1 \left.\right)^{2} > \left(\right. n^{k + 1} + 1 \left.\right) \left(\right. n^{k - 1} + 1 \left.\right) .\)

Xét hiệu:

\(\left(\right.n^{k}+1\left.\right)^2-\left(\right.n^{k+1}+1\left.\right)\left(\right.n^{k-1}+1\left.\right)=-n^{k-1}\left(\right.n-1\left.\right)^2<0\)

Vậy \(a_{k} < a_{k - 1}\), tức dãy \(\left(\right. a_{k} \left.\right)\) giảm dần theo \(k\)

Do đó:

\(A = a_{2022} < a_{2021} = B .\)

\(\Rightarrow B>A\)

Câu3

Ta đổi : \(27 = 3^{3}\), \(9 = 3^{2}\), \(125 = 5^{3}\).

\(\frac{5^{16} \cdot \left(\right. 3^{3} \left.\right)^{7}}{\left(\right. 5^{3} \left.\right)^{5} \cdot \left(\right. 3^{2} \left.\right)^{11}} = \frac{5^{16} \cdot 3^{21}}{5^{15} \cdot 3^{22}} = 5^{16 - 15} \cdot 3^{21 - 22} = \frac{5}{3} .\)

Vậy kết quả bằng \(\frac{5}{3}\).

Câu 3:

\(\frac{5^{16}\cdot27^7}{125^5\cdot9^{11}}\)

\(=\frac{5^{16}\cdot\left(3^3\right)^7}{\left(5^3\right)^5\cdot\left(3^2\right)^{11}}=\frac{5^{16}\cdot3^{21}}{5^{15}\cdot3^{22}}\)

\(=\frac53\)

Câu 2:

\(2022A=\frac{2022^{2023}+2022}{2022^{2023}+1}=1+\frac{2021}{2022^{2023}+1}\)

\(2022B=\frac{2022^{2022}+2022}{2022^{2022}+1}=1+\frac{2021}{2022^{2022}+1}\)

Ta có: \(2022^{2023}+1>2022^{2022}+1\)

=>\(\frac{2021}{2022^{2023}+1}<\frac{2021}{2022^{2022}+1}\)

=>\(\frac{2021}{2022^{2023}+1}+1<\frac{2021}{2022^{2022}+1}+1\)

=>2022A<2022B

=>A<B

Câu 1:

\(\left|x\right|\ge0\forall x\)

=>\(\left|x\right|+1\ge1\forall x\)

=>\(\left(\left|x\right|+1\right)^{10}\ge1^{10}=1\forall x\)

=>\(\left(\left|x\right|+1\right)^{10}+2023\ge1+2023=2024\forall x\)

Dấu '=' xảy ra khi x=0