Lời giải:

Đặt $2x-1=a$

\(a^6=a^8\\ \Leftrightarrow a^8-a^6=0\\ \Leftrightarrow a^6(a^2-1)=0\\ \Leftrightarrow a^6=0\text{ hoặc } a^2-1=0\\ \Leftrightarrow a=0 \text{ hoặc } a=\pm 1\\ \Leftrightarrow 2x-1=0 \text{ hoặc } 2x-1=1 \text{ hoặc } 2x-1=-1\)

$\Leftrightarrow x=\frac{1}{2}$ hoặc $x=1$ hoặc $x=0$

Nhận xét: Mũ chẵn và chung cơ số

⇒ Cơ số ϵ { -1; 1; 0}

Ta lập bảng:

⇒ x ϵ {0; 1}

Lời giải:

$f(x)=x^{6n}-x^{3n}+1=x^{3n}(x^{3n}-1)+1$

$=x^{3n}[(x^3)^n-1^n]+1$

$=x^{3n}(x^3-1)[(x^3)^{n-1}+(x^3)^{n-2}+...+1]+1$

$=x^{3n}(x^2+x+1)(x-1)[(x^3)^{n-1}+(x^3)^{n-2}+...+1]+1$

$\Rightarrow f(x)$ chia $x^2+x+1$ dư $1$

$\Rightarrow f(x)$ không chia hết cho $g(x)$

\(\left(x-2\right)^3-\left(x-2\right)\left(x^2+2x+4\right)=0\\ \Leftrightarrow\left(x-2\right)\left[\left(x-2\right)^2-\left(x^2+2x+4\right)\right]=0\\ \Leftrightarrow\left(x-2\right)\left(x^2-4x+4-x^2-2x-4\right)=0\\ \Leftrightarrow\left(x-2\right).\left(-6x\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\-6x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\)

Cách làm khác:

\(\left(x-2\right)^3-\left(x-2\right)\left(x^2+2x+4\right)=0\\ \Leftrightarrow x^3-3.x^2.2+3.x.2^2-2^3-\left(x^3-2^3\right)=0\\ \Leftrightarrow x^3-6x^2+12x-8-x^3+8=0\\ \Leftrightarrow-6x^2+12x=0\\ \Leftrightarrow-6x\left(x-2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)

Bạn viết lại đề bài nhé, mình ko hiểu bạn đang viết j

ĐK: \(\left\{{}\begin{matrix}x\ne2\\x\ne-1\end{matrix}\right.\)

PT trở thành:

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

[Không biết mình làm có đúng không ạ!]

1- London is visited by thousands of people every year.

2- The thief is arrested by police cars.

3- CO2 is absorbed by trees.

4- Photos are taken by Jane.

5- A lot of waste is produced by people.

6- The animals are fed by the farmers.

7- Films are watched by Mr. Jones.

8- English is spoken by the people.

9- Comics are read by him.

10- Volleyball is played by us.

11- The song is sung by them.

12- Photos are taken by me.

13- Poems are written by the writer.

14- The children are helped by the police.

15- The flowers are watered by mother.

16- The car is washed by my husband.

17- Halloween is loved by people around the world.

18- Blue shoes are worn by the teachers.

19- The school is cleaned by the janitor.

20- The house is cleaned by my mother everyday.

Bạn nào thấy sai thì chỉ mình nhaa, mình cảm ơn ạaa~~

Vì \(S.MNP\) là hình chóp tam giác đều 

nên \(SM=SN=SP=5\left(cm\right)\) và \(\triangle MNP\) đều (t/c)

\(\Rightarrow\left\{{}\begin{matrix}MN=NP=PM=10\left(cm\right)\\\widehat{MNP}=\widehat{NPM}=\widehat{PMN}=60^{\circ}\end{matrix}\right.\)