\(H=\left(3x-6\right)^2-3\left|2x-4\right|+2023\)

\(=\left(3x-6\right)^2-2\left|3x-6\right|+2023\)

\(=\left(3x-6\right)^2-2\left|3x-6\right|+1+2022\)

\(=\left(\left|3x-6\right|-1\right)^2+2022\)

Do \(\left(\left|3x-6\right|-1\right)^2\ge0;\forall x\)

\(\Rightarrow H\ge2022\)

\(\Rightarrow H_{min}=2022\) khi \(\left|3x-6\right|-1=0\Rightarrow x=\left\{\dfrac{7}{3};\dfrac{5}{3}\right\}\)

pip install pygame

A = \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) + \(\dfrac{2}{7.9}\) + ... + \(\dfrac{2}{19.21}\)

A = \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{9}\) + ... + \(\dfrac{1}{19}\) - \(\dfrac{1}{21}\)

A = \(\dfrac{1}{3}\) - \(\dfrac{1}{21}\)

A = \(\dfrac{2}{7}\)

Lời giải:

$x+x+58^0=180^0$ (tổng 3 góc trong tam giác)

$\Rightarrow 2x=180^0-58^0=122^0$

$\Rightarrow x=61^0$
--------------------

$x=\widehat{NMQ}+\widehat{MNQ}=30^0+65^0=95^0$

$y=180^0-30^0-x=150^0-95^0=55^0$

--------------------

$x=360^0-55^0-90^0-90^0=125^0$

bạn xem lại đề bài.

\(\left(2x+4\right)^{2024}+\left(\left|3y-9\right|\right)^{2023}=0\) (*) 

Ta có: \(\left(2x+4\right)^{2024}\ge0\forall x\) (vì có số mũ chẵn) (1)

\(\left(\left|3y-9\right|\right)^{2023}\ge0\forall y\) (vì giá trị tuyệt đối luôn ≥0) (2) 

Từ (1) và (2) ta có: 

\(\Rightarrow\left\{{}\begin{matrix}2x+4=0\\3y-9=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=-2\\y=3\end{matrix}\right.\)

Vậy: ... 

tại sao 3y-9=0 mà y lại = 3

Ta có:

\(VT=\left|2x+3\right|+\left|1-2x\right|\ge\left|2x+3+1-2x\right|=4\)

Mặt khác do \(\left(x+1\right)^2\ge0;\forall x\) nên:

\(VP=\dfrac{8}{3\left(x+1\right)^2+2}\le\dfrac{8}{3.0+2}=4\)

\(\Rightarrow VT\ge VP\)

Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}\left(2x+3\right)\left(1-2x\right)\ge0\\\left(x+1\right)^2=0\end{matrix}\right.\)

\(\Rightarrow x=-1\)

Ta có VT: \(\left|2x+3\right|+\left|2x-1\right|=\left|2x+3\right|+\left|1-2x\right|\)

Áp dụng bđt: \(\left|a\right|+\left|b\right|\ge\left|a+b\right|\)  

\(\Rightarrow\left|2x+3\right|+\left|1-2x\right|\ge\left|2x+3+1-2x\right|=4\) (1)

VP: \(\dfrac{8}{3\left(x+1\right)^2+2}\le\dfrac{8}{3\cdot0+2}=\dfrac{8}{2}=4\) (2) 

Từ (1) và (2) để 2 vế bằng nhau thì:

Dấu "=" xảy ra khi: 

\(\left\{{}\begin{matrix}x+1=0\\\left(2x+3\right)\left(1-2x\right)\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=-1\\-\dfrac{3}{2}\le x\le\dfrac{1}{2}\end{matrix}\right.\)

Vậy x = -1 giá trị thỏa mãn 

Ta có: \(\left\{{}\begin{matrix}\left|x-3\right|\ge0\forall x\\\left|y+3\right|\ge0\forall y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(\left|x-3\right|+2\right)^2\ge2^2=4\forall x\\\left|y+3\right|\ge0\forall y\end{matrix}\right.\)

\(\Rightarrow\left(\left|x-3\right|+2\right)^2+\left|y+3\right|\ge4\forall x,y\)

\(\Rightarrow P=\left(\left|x-3\right|+2\right)^2+\left|y+3\right|+2018\ge4+2018=2022\forall x,y\)

Dấu \("="\) xảy ra khi: \(\left\{{}\begin{matrix}x-3=0\\y+3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-3\end{matrix}\right.\)

Vậy \(Min_P=2022\) khi \(x=3;y=-3\).