Tìm x biết: x+1/9=8/x-1
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PH
1
N
2 tháng 8 2017
\(x+\frac{1}{5}+x+\frac{1}{6}+x+\frac{1}{7}=x+\frac{1}{8}+x+\frac{1}{9}\)
\(3x+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}=2x+\frac{1}{8}+\frac{1}{9}\)
\(3x+\frac{107}{210}=2x+\frac{17}{72}\)
\(3x-2x=\frac{17}{72}-\frac{107}{210}\)
\(x=\frac{-689}{2520}\)
Vậy \(x=\frac{-689}{2520}\).
15 tháng 7 2017
\(\frac{x+1}{9}+\frac{x+2}{8}+\frac{x+3}{7}+...+\frac{x+9}{1}=-9\)
\(\left(\frac{x+1}{9}+1\right)+\left(\frac{x+2}{8}+1\right)+\left(\frac{x+3}{7}+1\right)+...+\left(\frac{x+9}{1}+1\right)=0\)
\(\frac{x+10}{9}+\frac{x+10}{8}+\frac{x+10}{7}+...+\frac{x+10}{1}=0\)
\(\left(x+10\right).\left(\frac{1}{9}+\frac{1}{8}+\frac{1}{7}+...+1\right)=0\)
vì \(\frac{1}{9}+\frac{1}{8}+\frac{1}{7}+...+1\ne0\)
\(\Rightarrow x+10=0\)
\(\Rightarrow x=-10\)
NT
0
29 tháng 11 2023
1: 7-x=8+(-7)
=>7-x=8-7=1
=>x=7-1=6
2: \(x-8=\left(-3\right)-8\)
=>x-8=-11
=>\(x=-11+8=-3\)
3: \(2-x=10-9+23\)
=>\(2-x=33-9=24\)
=>x=2-24=-22
4: \(-2-x=15\)
=>\(x=-2-15=-17\)
5: \(-7+x-8=-3-1+13\)
=>x-14=13-4=9
=>x=9+14=23
6: 100-x+7=-x+3
=>107-x=3-x
=>107=3(vô lý)
7: \(23+x=8-2x\)
=>\(x+2x=8-23\)
=>3x=-15
=>x=-15/3=-5
NT
2
Ta có: \(x+\frac{1}{9}=\frac{8}{x}-1\)
\(\Leftrightarrow x-\frac{8}{x}=-1-\frac{1}{9}\)
\(\Leftrightarrow\frac{x^2-8}{x}=-\frac{10}{9}\)
\(\Leftrightarrow9.\left(x^2-8\right)=-10x\)
\(\Leftrightarrow9x^2+10x-72=0\)
\(\Leftrightarrow\left(9x^2+10x+\frac{25}{9}\right)-\frac{673}{9}=0\)
\(\Leftrightarrow\left(3x+\frac{5}{3}\right)^2=\frac{673}{9}\)
\(\Leftrightarrow3x+\frac{5}{3}=\pm\frac{\sqrt{673}}{3}\)
+ \(3x+\frac{5}{3}=\frac{\sqrt{673}}{3}\)\(\Leftrightarrow\)\(3x=\frac{\sqrt{673}-5}{3}\)
\(\Leftrightarrow\)\(x=\frac{\sqrt{673}-5}{9}\)
+ \(3x+\frac{5}{3}=-\frac{\sqrt{673}}{3}\)\(\Leftrightarrow\)\(3x=\frac{-\sqrt{673}-5}{3}\)
\(\Leftrightarrow\)\(x=\frac{-\sqrt{673}-5}{9}\)
Vậy \(x\in\left\{\frac{\sqrt{673}-5}{9};\frac{-\sqrt{673}-5}{9}\right\}\)
Ta có : \(\frac{x+1}{9}=\frac{8}{x-1}\left(x\ne1\right)\)
\(\Rightarrow\left(x+1\right).\left(x-1\right)=8.9\)
\(\Rightarrow x^2-1=72\Rightarrow x^2=73\Rightarrow x=\pm\sqrt{73}\)