Ta có: A=2023x2022+2023+2022A=x2022+20232023​+2022

Lại có: x2022≥0∀xx2022≥0∀x

⇔x2022+2023≥2023∀x⇔x2022+2023≥2023∀x

⇔1x2022+2023≤12023∀x⇔x2022+20231​≤20231​∀x

⇔2023x2022+2023+2022≤20232023+2022=2023∀x⇔x2022+20232023​+2022≤20232023​+2022=2023∀x

$\iff A\le 2023\forall x$

Dấu $"="$ xảy ra khi: x2022=0⇔x=0x2022=0⇔x=0

Vậy MaxA=2023MaxA​=2023 tại $x=0$.

Kẻ tia $Cx$ là tia phân giác của $\widehat{ACD}$ và $Dy$ là tia phân giác của $\widehat{BDC}$, hai tia $Cx$ và $Dy$ cắt nhau tại $E$.

$\widehat{C_1}=\widehat{C_2}={60}^{\circ }$ và $\widehat{D_1}=\widehat{D_2}={30}^{\circ }$

Kẻ tia $Ez//m//n$, tính $\widehat{E_1}={60}^{\circ }$ và $\widehat{E_2}={30}^{\circ }$

Suy ra $\widehat{CED}={90}^{\circ }$.

$a)\text{hept}\{\begin{array}{l}\text{Ta coˊ:}\widehat{A^4}=\widehat{B^2}=110^0\\ \text{Maˋ chuˊng so le trong}\end{array}$

$\Rightarrow a//b$

$b)\text{hept}\{\begin{array}{l}\text{Ta coˊ:}c\perp a\left(gt\right)\\ \text{Maˋ }a//b\left(cmt\right)\end{array}$

$\Rightarrow c\perp b$

$c)\text{Ta coˊ:}\widehat{B^1}+\widehat{B^2}=180^0\left(\text{keˆˋ buˋ}\right)$

$\Rightarrow \widehat{B^1}=180^0-\widehat{B^2}$

$\Rightarrow \widehat{B^1}=180^0-110^0=70^0$

$\text{Ta coˊ:}\widehat{B^1}=\widehat{B^3}=70^0\left(\text{đoˆˊi đỉnh}\right)$

$\text{Ta coˊ:}\widehat{B^3}=\widehat{C^3}\left(\text{Đoˆˋng vị}\right)$

$\Rightarrow \widehat{B^3}=\widehat{C^3}=70^0$

$a)\text{hept}\{\begin{array}{l}\text{Ta coˊ:}\widehat{A^4}=\widehat{B^2}=110^0\\ \text{Maˋ chuˊng so le trong}\end{array}$

$\Rightarrow a//b$

$b)\text{hept}\{\begin{array}{l}\text{Ta coˊ:}c\perp a\left(gt\right)\\ \text{Maˋ }a//b\left(cmt\right)\end{array}$

$\Rightarrow c\perp b$

$c)\text{Ta coˊ:}\widehat{B^1}+\widehat{B^2}=180^0\left(\text{keˆˋ buˋ}\right)$

$\Rightarrow \widehat{B^1}=180^0-\widehat{B^2}$

$\Rightarrow \widehat{B^1}=180^0-110^0=70^0$

$\text{Ta coˊ:}\widehat{B^1}=\widehat{B^3}=70^0\left(\text{đoˆˊi đỉnh}\right)$

$\text{Ta coˊ:}\widehat{B^3}=\widehat{C^3}\left(\text{Đoˆˋng vị}\right)$

$\Rightarrow \widehat{B^3}=\widehat{C^3}=70^0$

A4 và B2; A3 và B1