Bài 1:
a)Tìm x:
\(\frac{x+4}{2008}+\frac{x+3}{2009}=\frac{x+2}{2010}+\frac{x+1}{2011}\)
b) cho: \(M=\frac{1}{2}+\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3+\left(\frac{1}{2}\right)^4+...+\left(\frac{1}{2}\right)^{99}+\left(\frac{1}{2}\right)^{100}\)
Bài 2:
a) Tìm x,y biết:
\(\frac{x+2y}{18}=\frac{1+4y}{24}=\frac{1+x+6y}{6x}\)
b) tìm ssos nguyên n để A mang giá trị nguyên và tính giá trị đó
\(A=\frac{9+3n}{n-4}\)
1) a. Ta có:\(\frac{x+4}{2008}+\frac{x+3}{2009}=\frac{x+2}{2010}+\frac{x+1}{2011}\)
\(\Rightarrow\frac{x+4}{2008}+1+\frac{x+3}{2009}+1=\frac{x+2}{2010}+1+\frac{x+1}{2011}+1\)
\(\Rightarrow\frac{x+4+2008}{2008}+\frac{x+3+2009}{2009}=\frac{x+2+2010}{2010}+\frac{x+1+2011}{2011}\)
\(\Rightarrow\frac{x+2012}{2008}+\frac{x+2012}{2009}=\frac{x+2012}{2010}+\frac{x+2012}{2011}\)
\(\Rightarrow\left(x+2012\right)\left(\frac{1}{2008}+\frac{1}{2009}\right)=\left(x+2012\right)\left(\frac{1}{2010}+\frac{1}{2011}\right)\)
\(\Rightarrow\left(x+2012\right)\left(\frac{1}{2008}+\frac{1}{2009}\right)-\left(x+2012\right)\left(\frac{1}{2010}+\frac{1}{2011}\right)=0\)
\(\Rightarrow\left(x+2012\right)\left(\frac{1}{2008}+\frac{1}{2009}-\frac{1}{2010}-\frac{1}{2011}\right)=0\)
\(\Rightarrow x+2012=0\)
\(\Rightarrow x=-2012\)
Bài 2:
a.Ta có: \(\frac{x+2y}{18}=\frac{1+4y}{24}\)
\(\Rightarrow24x+48y=18+72y\)
\(\Rightarrow24x+48y-72y=18\)
\(\Rightarrow24x-24y=18\)
\(\Rightarrow24\left(x-y\right)=18\)
\(\Rightarrow x-y=\frac{3}{4}\)
\(\Rightarrow y=x-\frac{3}{4}\)
thay \(y=x-\frac{3}{4}\)vào \(\frac{1+4y}{24}=\frac{1+x+6y}{6x}\)ta được \(\frac{1+4\times\left(x-\frac{3}{4}\right)}{24}=\frac{1+x+6\times\left(x-\frac{3}{4}\right)}{6x}\)
giải ra ta được x=7
\(\Rightarrow y=7-\frac{3}{4}=\frac{25}{4}\)
b. Đẻ A mang giá trị nuyên
\(\Leftrightarrow9+3n⋮n-4\)
\(\Leftrightarrow3n-12+21⋮n-4\)
\(\Leftrightarrow3\left(n-4\right)+21⋮n-4\)
\(\Leftrightarrow21⋮n-4\)
\(\Leftrightarrow n-4\inƯ_{\left(21\right)}=\left\{\pm1;\pm3;\pm7;\pm21\right\}\)
Ta có bảng sau:
| n-4 | 1 | -1 | 3 | -3 | 7 | -7 | 21 |
-21 |
| n | 5 | 4 | 7 | 1 | 11 | -3 | 25 | -17 |
Vậy \(n\in\left\{5;4;7;1;11;-3;25;-17\right\}\)thì A là số nguyên.
Thay n vào A và tính giá trị
