Read the passage and answer the questions

Minh and Tuan are students at Nguyen Hue School in Ho Chi Minh City. There are twelve classrooms in this school. Minh is in class Six and Tuan is in class Seven. Minh’s father is a doctor, and Tuan’s father is a doctor, too. Tuan’s mother is a teacher. Minh and Tuan are good students at school.

Question: What does Tuan’s mother do?

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a)\(\left|x+1\right|-x+1=2\)

\(\Rightarrow\left|x+1\right|=1+x\)

\(\Rightarrow\left[{}\begin{matrix}x+1=-1-x\\x+1=1+x\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x=0\end{matrix}\right.\)

b)\(\left|x+1\right|=\left|2x+3\right|\)

\(\Rightarrow\left|x+1\right|-\left|2x+3\right|=0\)

Mà |x+1|\(\ge0\);\(\left|2x-3\right|\ge0\)

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

\(\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+...+\dfrac{1}{100.103}\)

\(=\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{100}-\dfrac{1}{103}\)

\(=\dfrac{1}{1}-\dfrac{1}{103}\)

\(=\dfrac{102}{103}\)

Ta có:\(\left|x\left(x+2\right)\right|=x\)

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

Vậy \(x\in\left\{-3;-1\right\}\)

Tính bằng hai cách:

a) \(7^6:7^2=7^5\)

b)\(16^2:4^2=4^2\)

c)\(25^2:5^2=5^2\)

d)\(3^2:9^3=3^2:3^6=3^{-4}\)

4,5*2,5-x*2=1,25

11,25-x*2=1,25

        x*2=11,25-1,25      

         x*2=10

        x=10:2=5

Tick mình nhé các bạn

a)\(\dfrac{x-1}{x+5}=\dfrac{6}{7}\)

\(\Rightarrow6x+30=7x-7\)

\(\Rightarrow7+30=7x-6x\)

\(\Rightarrow x=37\)

Vậy x=37

b)\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)

\(\Rightarrow\left(x-1\right)^{x+2}-\left(x-1\right)^{x+4}=0\)

\(\Rightarrow\left(x-1\right)^{x+2}\left[1-\left(x-1\right)^2\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-1\right)^{x+2}=0\\1-\left(x-1\right)^2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

Vậy \(x\in\left\{1;2\right\}\)

\(x^{10}=x\)

\(\Rightarrow x^{10}-x=0\)

\(\Rightarrow x\left(x^9-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x^9-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

Vậy x \(\in\left\{0;1\right\}\)

18.1+4+7+10+13+16+19+...+.97+100

=18+(100+1)((100-1);3+1):2

=18+1717

=1735