\(\left[a-\left(b+c\right)\right]^2=a^2-2a\left(b+c\right)+\left(b+c\right)^2=a^2-2ab-2ac+b^2+2bc+c^2\)

\(D=x^2+2x+1+y^2-4y+4+2023=\left(x+1\right)^2+\left(y-2\right)^2+2023\ge2023\)

Dấu ''='' xảy ra khi x = -1 ; y = 2 

Bài 6 

Ta có ^A + ^B + ^C + ^D = 360⁰ 

=>  ^A + ^B = 360⁰ - ^C - ^D = 220⁰

=> \(\left\{{}\begin{matrix}A+B=220\\A-B=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}A=115^0\\B=105^0\end{matrix}\right.\)

Bài 4 : 

a, ^ABC = 180⁰ - ^B = 180⁰ - 75⁰ = 105⁰ 

b, Ta có ^A + ^B + ^C + ^D = 360⁰ 

=> ^DAB = 360⁰ - ^B - ^C - ^D = 90⁰ 

=> ^A1 = 90⁰

Bài 5 

Theo tc dãy tỉ số bằng nhau 

\(\dfrac{A}{1}=\dfrac{B}{2}=\dfrac{C}{3}=\dfrac{D}{4}=\dfrac{A+B+C+D}{1+2+3+4}=\dfrac{360^0}{10}=36^0\Rightarrow A=36^0;B=72^0;C=108^0;D=144^0\)

\(32+56+4x=200x\Leftrightarrow88+4x=200x\Leftrightarrow196x=88\Leftrightarrow x=\dfrac{22}{49}\)

Số hs chỉ chơi 1 môn thể thao 

25 + 23 - 14  = 34 bn 

\(M=2\left(x-3\right)-x+4=2x-6-x+4=x-2\)

a, \(3\left(x+2\right)-1=4\left(x-1\right)\Leftrightarrow3x+6-1=4x-4\Leftrightarrow x=5+4=9\)

b, \(5-2\left(x-3\right)=3\left(x+1\right)+4\Leftrightarrow5-2x+6=3x+3+4\Leftrightarrow-2x+11=3x+7\Leftrightarrow5x=4\Leftrightarrow x=\dfrac{4}{5}\)

c, \(\dfrac{x+1}{3}-4=\dfrac{2x-1}{2}\Rightarrow2x+2-24=3\left(2x-1\right)\Leftrightarrow2x-22=6x-3\Leftrightarrow4x=-19\Leftrightarrow x=-\dfrac{19}{4}\)

d, \(\dfrac{x-2}{4}+2x=\dfrac{x-1}{3}\Rightarrow3\left(x-2\right)+24x=4\left(x-1\right)\)

\(\Leftrightarrow3x-6+24x=4x-4\Leftrightarrow23x=2\Leftrightarrow x=\dfrac{2}{23}\)

\(-M=-2xz^2+xy^2-xy-3z^2-2xy^2-xz^2+xy=-3xz^2-xy^2-3z^2\)

\(\Rightarrow M=3xz^2+xy^2+3z^2\)

sửa \(\dfrac{2}{1.4}+\dfrac{2}{4.7}+...+\dfrac{2}{2022.2023}\)

\(=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{2022}-\dfrac{1}{1023}\right)=\dfrac{2}{3}.\left(1-\dfrac{1}{2023}\right)=\dfrac{2.2022}{3.2023}=\dfrac{1348}{2023}\)