Xét tam giác MAE và tam giác EBC ... =>tam giác MAE = tam giác CBE (c-g-c)

=> AM=BC(...)(1)

và góc M= góc MCB (..)

=> AM//BC(3)

Xét tam giác ADN và tam giác DBC ...=> tam giác ADN = tam giác CDB (c-g-c)

=> AN=CB (...)(2)

và góc N = góc NBC (...)

=> AN//BC(4)

Từ (1) và (2) => AN=AM(5)

Từ(4) và (3) => A , M , N thẳng hàng ( tiên đề Ơ-clit )(6)

Từ (5) và (6) => A là trung điểm của MN

Ta có: \(x^2\ge0;\left|x+y\right|\ge0;\forall x,y\)

=> \(M=2015+3\left(x^2+1\right)^{2016}+\left|x+y\right|^{2017}\)

\(\ge2015+3\left(0+1\right)^{2016}+0^{2017}=2018\)

Dấu "=" xảy ra khi và chỉ khi: \(\hept{\begin{cases}x^2=0\\\left|x+y\right|=0\end{cases}\Leftrightarrow x=y=0}\)

Vậy gtnn của M = 2018 đạt tại x = y = 0.

=>2013= |x-4+10-x+x+101+999-x+x+1000|

rồi cộng lại đc bn + x

rồi chia Th ra

Xét VP = \(\left(\left|x-4\right|+\left|x+999\right|\right)+\left(\left|x-10\right|+\left|x+1000\right|\right)+\left|x+101\right|\)

\(\ge\left|x+999+4-x\right|+\left|x+1000+10-x\right|+\left|x+101\right|\)

\(=2013+\left|x+101\right|\ge2013=VT\)

=> VP \(\ge\)VT

Dấu "=" xảy ra <=>\(\hept{\begin{cases}\left(x+999\right)\left(4-x\right)\ge0\\\left(x+1000\right)\left(10-x\right)\ge0\\x+101=0\end{cases}}\)<=> x = -101

Vậy VP = VT <=> x = -101

1. I have many hobbies to fill my free time. I to draw pictures of my niece on my phone. Sometimes, I make Karaoke videos so I can sing when I'm bored. I also to fix clothes for other people. I often go on olm.vn to answer English questions. Last but not least, I to translate books or website content from English to Vietnamese and vice versa.

2. I think I should drink water more because 75% of the human body is made up of water. I need to eat for veggies and fruits. I also need to eat three meals a day instead of having brunch and dinner only. 

3. Community service is when you go out to serve your community by doing a variety of activities, such as picking up trash, mowing the neighbor lawns. To change the world, I'd to translate the books of intelligent people to Vietnamese to improve the Vietnamese folks' knowledge. 

4. I prefer art over music because I to do things with my fingers and put my imagination onto paper. 

5. My favorite food is deep-fry duck. You just need to fill a large pot with oil, bring it up to 450 Farenheight degree. Then you put the spices all over the duck before you deep fry the duck in the pot. After an hour and half, check the temp to see if the duck is thoroughly cooked. When the duck is fully cooked, take it out and get ready to chow it down. 

       \(3,8:2x=\frac{1}{4}:\frac{8}{3}\)

      \(3,8:2x=\frac{1}{4}\cdot\frac{3}{8}\)

      \(3,8:2x=\frac{3}{32}\)

      \(2x=3,8:\frac{3}{32}\)

      \(2x=\frac{19}{5}\cdot\frac{32}{3}\)

\(\frac{1}{4}:x=-\frac{7}{20}\)

\(x=\frac{1}{4}.-\frac{20}{4}\)

\(x=-\frac{5}{4}\)

theo tính chất dãy tỉ số bằng nhau có

\(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}=\frac{x+y+z}{2+3+5}=\frac{24}{10}=\frac{12}{5}\)

\(\Rightarrow\frac{x}{2}=\frac{12}{5}\Rightarrow x=2.12:5=\frac{24}{5}\)

\(\Rightarrow\frac{y}{3}=\frac{12}{5}\Rightarrow y=3.12:5=\frac{36}{5}\)

\(\Rightarrow\frac{z}{5}=\frac{12}{5}\Rightarrow z=5.12:5=12\)

Ta có : x/2=y/3=z/5 và điều kiện :x+y+z=24 

Áp dụng tính chất dãy tỉ số bằng nhau : 

x/2=y/3=z/5 =x+y+z/2+3+5 =24/10=12/5

Suy ra : 12/5.2=24/5

               12/5.3=36/5

                 12/5.5=12

  Vậy (x;y;z)= (24/5;36/5;12)