Question

[Trần Thu Trang]

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

\(A=\frac{9+3n}{n-4}\)

Answer 1

[Ha Hoang Vu Nhat]

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