Tìm x biết: (1/5 - 3/2 . x)2= 9/4
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3^{-1}\cdot3^n+4\cdot3^n=13\cdot3^5\)
=> \(\frac{1}{3}\cdot3^n+4\cdot3^n=13\cdot3^5\)
=> \(3^n\left[\frac{1}{3}+4\right]=13\cdot3^5\)
=> \(3^n\cdot\frac{13}{3}=13\cdot3^5\)
=> \(3^n=\frac{13\cdot3^5}{\frac{13}{3}}=729\)
=> \(3^n=3^6\)
=> n = 6
Vậy giá trị của n cần tìm là 6
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
\(\Rightarrow\frac{3}{4}A=\frac{3}{4}-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^2+-\left(\frac{3}{4}\right)^4+...+\left(\frac{3}{4}\right)^{2010}-\left(\frac{3}{4}\right)^{2011}\)
\(\Rightarrow\frac{3}{4}A+A=\frac{3}{4}-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^2+-\left(\frac{3}{4}\right)^4+...+\left(\frac{3}{4}\right)^{20010}-\left(\frac{3}{4}\right)^{2011}\)
\(+1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
\(\Rightarrow\frac{7}{4}A=1-\left(\frac{3}{4}\right)^{2011}\)
\(\Rightarrow A=\frac{4}{7}-\frac{4}{7}.\left(\frac{3}{4}\right)^{2011}\)
\(\Rightarrow A=\frac{4}{7}-\frac{3^{2011}}{7.4^{2010}}\)
Vậy A không là số tự nhiên
Bài làm
Vì \(\left(\frac{1}{5}-\frac{3}{2}.x\right)^2=\frac{9}{4}\)
\(\Rightarrow\left(\frac{1}{5}-\frac{3}{2}.x\right)^2=\left(\frac{3}{2}\right)^2\)
\(\Rightarrow\frac{1}{5}-\frac{3}{2}x=\frac{3}{2}\)
\(\Rightarrow\frac{3}{2}x=\frac{1}{5}-\frac{3}{2}\)
\(\Rightarrow\frac{3}{2}x=\frac{2}{10}-\frac{15}{10}\)
\(\Rightarrow\frac{3}{2}x=-\frac{13}{10}\)
\(\Rightarrow x=-\frac{13}{10}.\frac{2}{3}\)
\(\Rightarrow x=-\frac{13}{15}\)
Vậy \(x=-\frac{13}{15}\)
\(\left(\frac{1}{5}-\frac{3}{2}\cdot x\right)^2=\frac{9}{4}\)
\(\orbr{\begin{cases}\frac{1}{5}-\frac{3}{2}\cdot x=\frac{3}{2}\\\frac{1}{5}-\frac{3}{2}\cdot x=-\frac{3}{2}\end{cases}}\)
\(\orbr{\begin{cases}\frac{3}{2}\cdot x=\frac{1}{5}-\frac{3}{2}=-\frac{13}{10}\\\frac{3}{2}\cdot x=\frac{1}{5}-\left(-\frac{3}{2}\right)=\frac{1}{5}+\frac{3}{2}=\frac{17}{10}\end{cases}}\)
\(\orbr{\begin{cases}x=-\frac{13}{10}:\frac{3}{2}=-\frac{13}{10}\cdot\frac{2}{3}=-\frac{13}{15}\\x=\frac{17}{10}:\frac{3}{2}=\frac{17}{10}\cdot\frac{2}{3}=\frac{17}{15}\end{cases}}\)
Vậy \(x=-\frac{13}{15}\)hoặc \(x=\frac{17}{15}\)