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

\(\left(x-6\right)^3-\left(x-6\right)^2\)

\(\left(x-6\right)^2\left(x-6-1\right)=0\)

\(\left(x-6\right)^2\left(x-7\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-6\right)^2=0\\\\x-7=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x-6=0\\\\x=7\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=6\\\\x=7\end{matrix}\right.\)

Vậy \(x=6;x=7\)

\(3+2^{x-1}=24-\left[4^2-\left(2^2-1\right)\right]\)

\(=3+2^{x-1}=24-\left[4^2-\left(4-1\right)\right]\)

\(=3+2^{x-1}=24-\left[16-3\right]\)

\(\Rightarrow3+2^{x-1}=11\)

\(\Rightarrow2^{x-1}=11-3\)

\(\Rightarrow2^{x-1}=8\)

\(\Rightarrow2^{x-1}=2^3\)

\(\Rightarrow x-1=3\)

\(\Rightarrow x=4\)

Vậy \(x=4\)

\(275:25=11:100=\dfrac{11}{100}=0,11\)

Vần liền:

 - Vần liền là vần được gieo liên tiếp ở các dòng thơ, ca dao, tục ngữ.

Vần cách:

 - Vần cách là vần không gieo liên tiếp mà thường cách ra một dòng thơ ở ca dao, tục ngữ.

a) \(\left(x^2-7x+12\right).\left(x^2-15x+56\right)-60\)

\(=\left(x-3\right)\left(x-4\right)\left(x-7\right)\left(x-8\right)-60\)

b) \(x^4+2000x^2+1999x+2000\)

\(=\left(x^2-x+2000\right)\left(x^2+x+1\right)\)

\(=\left(x^2+x-1\right)^2+1999\left(x^2+x+1\right)+1\)

Từ nào dưới đây không đồng nghĩa với các từ còn lại?

A. dũng cảm  B. dũng sĩ  C. gan dạ  D. can đảm

Ta có: \(a.b=ƯCLN\left(a,b\right)\times BCNN\left(a,b\right)\)

Mà \(a.b=2940\) và \(BCNN\left(a,b\right)=210\)

\(\LeftrightarrowƯCLN\left(a,b\right)=2940:210=14\)

\(\Rightarrow a=14m,b=14n\left(m;n>0\right)\)

Thay \(a=14m;b=14n\) vào \(a.b=2940\) ta được:

\(14m.14n=2940\)

\(\Leftrightarrow196.m.n=2940\)

\(\Leftrightarrow m.n=15\)

\(\Leftrightarrow m;n\inƯ\left(15\right)=\left\{1;3;5;15\right\}\)

\(+\) Với \(m=1;n=15\Rightarrow a=14;b=210\)

\(+\) Với \(m=3;n=5\Rightarrow a=42;b=70\)

\(+\) Với \(m=5;n=3\Rightarrow a=70;b=42\)

\(+\) Với \(m=15;n=1\Rightarrow a=210;b=14\)

Vậy \(\left(a,b\right)\in\left[\left(14;210\right);\left(42;70\right);\left(70;42\right);\left(210;14\right)\right]\)

Vì \(BCNN\left(a,b\right)=300\) và \(ƯCLN\left(a,b\right)=15\)

\(\Leftrightarrow a.b=300.15=4500\)

Vì \(ƯCLN\left(a,b\right)=15\) nên \(a=15m\) và \(b=15n\) với \(ƯCLN=\left(m,n\right)=1\)

Vì \(a+15=b\Rightarrow15m+15=15n\Rightarrow15\left(m+1\right)=15n\)

\(\Leftrightarrow m+1=n\)

Mà \(a.b=4500\Rightarrow15m.15n=4500\Rightarrow15.15.m.n=4500\)

\(\Leftrightarrow m.n=20\)

\(\Leftrightarrow m=1\) và \(n=20\) hoặc \(m=4\) và \(n=5\)

1. It is necessary that everyone be here on time.
-> It is necessary for everyone to be here on time.
2. The bookshop is opposite the post office.
-> The bookshop is across from the post office.
3. Jimmy doesn't have an IELTS certificate. He can't get a job.
-> If Jimmy had an IELTS certificate, he could get a job.
4. She didn't know anything about the new project.
-> She had no knowledge about the new project.
5. Despite the bad weather, I still enjoyed the week.
-> Despite the bad weather, I still enjoyed the week.