Bạn tham khảo ở đây nhé: https://olm.vn/hoi-dap/detail/211418926066.html

Ta có : \(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)

\(\Rightarrow\left(x-7\right)^{x+11}-\left(x-7\right)^{x+1}=0\)

\(\Rightarrow\left(x-7\right)^{x+1}.\left[\left(x-7\right)^{x+10}-1\right]=0\)

\(\Rightarrow\hept{\begin{cases}\left(x-7\right)^{x+1}=0\\\left(x-7\right)^{x+10}=1\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x-7=0\\x-7=1\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x=7\\x=8\end{cases}}\)

Gọi 3 đường cao là a,b,c. Ta có: \(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}\)và c - a = 9cm

Áp dụng dãy tỉ số bằng nhau: \(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}=\frac{c-a}{4-2}=\frac{9}{2}\)

 =>\(a=\frac{9}{2}\cdot2=9\left(cm\right)\)

\(b=\frac{9}{2}\cdot3=\frac{27}{2}\left(cm\right)\)

\(c=\frac{9}{2}\cdot4=18\left(cm\right)\)

Vậy chu vi tam giác là: \(9+\frac{27}{2}+18=\frac{18}{2}+\frac{27}{2}+\frac{36}{2}=\frac{81}{2}\left(cm\right)\)

\(A=(1-\frac{1}{1+2})(1-\frac{1}{1+2+3})(1-\frac{1}{1+2+3+4})...(1-\frac{1}{1+2+3+...+2006})\)

\(A=(1-\frac{1}{3})(1-\frac{1}{6})(1-\frac{1}{10})...(1-\frac{1}{2013021})\)

\(A=\frac{2}{3}\cdot\frac{5}{6}\cdot\frac{9}{10}....\frac{2013020}{2013021}\)

Sorry bạn máy tính mình có chút vấn đề để mk làm tiếp :

\(A=\frac{4}{6}\cdot\frac{10}{12}\cdot\frac{18}{20}....\cdot\frac{4026040}{4026042}\)

\(A=\frac{1\cdot4}{2\cdot3}\cdot\frac{2\cdot5}{3\cdot4}\cdot\frac{3\cdot6}{4\cdot5}\cdot...\cdot\frac{2005\cdot2008}{2006\cdot2007}\)

\(A=\frac{1\cdot2\cdot3\cdot...\cdot2005}{2\cdot3\cdot4\cdot...\cdot2006}\cdot\frac{4\cdot5\cdot6\cdot...\cdot2008}{3\cdot4\cdot5\cdot...\cdot2007}\)

\(A=\frac{1}{2006}\cdot\frac{2008}{3}=\frac{1004}{3009}\)

P/S : Hoq chắc :>