Question

giúp mk vs:

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

c)so sánh: \(2^{300}\) và \(3^{200}\)

Answer 1

c) Ta có: \(2^{300}=\left(2^3\right)^{100}=8^{100};3^{200}=\left(3^2\right)^{100}=9^{100}\)

Vì \(8^{100}< 9^{100}\Rightarrow2^{300}< 3^{200}\)

Answer 2

t làm câu 1.you viết đề sai nhé

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

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

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

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

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

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

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