Tìm x,y,z thuộc Z biết:
\(\frac{3}{x-5}=\frac{-4}{x+2}\) \(\frac{-4}{8}=\frac{x}{-10}=\frac{-7}{x}=\frac{z}{-24}\) \(-\frac{42}{7}< x< -\frac{24}{6}\)
\(\frac{x}{-2}=\frac{-8}{x}\) \(\frac{-28}{4}\le x\le\frac{-21}{7}\) \(\frac{-2}{x}=\frac{y}{3}\) \(\frac{2x-9}{240}=\frac{39}{80}\)
\(\frac{-8}{15}< \frac{x}{40}< \frac{-7}{15}\)
\(\frac{3}{x-5}=-\frac{4}{x+2}\)
\(\Leftrightarrow3\left(x+2\right)=-4\left(x-5\right)\)
\(\Leftrightarrow3x+6=-4x+20\)
\(\Leftrightarrow7x=14\)
\(\Leftrightarrow x=2\)
\(\frac{x}{-2}=-\frac{8}{x}\)
\(\Leftrightarrow x^2=16\)
\(\Leftrightarrow x=\pm4\)
\(-\frac{2}{x}=\frac{y}{3}\)
\(\Leftrightarrow xy=-6\)
\(\Leftrightarrow x;y\inƯ\left(-6\right)=\left\{\pm1;\pm2;\pm3;\pm6\right\}\)
Xét bảng
| x | 1 | -1 | 2 | -2 | 3 | -3 | 6 | -1 |
| y | -6 | 6 | -3 | 3 | -2 | 2 | -1 | 6 |
Vậy.................
\(\frac{2x-9}{240}=\frac{39}{80}\)
\(\Leftrightarrow2x-9=\frac{240.39}{80}\)
\(\Leftrightarrow2x-9=117\)
\(\Leftrightarrow2x=126\)
\(\Leftrightarrow x=63\)
