Question

[Mạc Hy]

Tìm x,y,z thuộc Z biết:

\(\frac{3}{x-5}=\frac{-4}{x+2}\)                 \(\frac{-4}{8}=\frac{x}{-10}=\frac{-7}{x}=\frac{z}{-24}\)           \(-\frac{42}{7}< x< -\frac{24}{6}\)

\(\frac{x}{-2}=\frac{-8}{x}\)                      \(\frac{-28}{4}\le x\le\frac{-21}{7}\)          \(\frac{-2}{x}=\frac{y}{3}\)         \(\frac{2x-9}{240}=\frac{39}{80}\)

\(\frac{-8}{15}< \frac{x}{40}< \frac{-7}{15}\)

Answer 1

[Đặng Tú Phương]

\(\frac{3}{x-5}=-\frac{4}{x+2}\)

\(\Leftrightarrow3\left(x+2\right)=-4\left(x-5\right)\)

\(\Leftrightarrow3x+6=-4x+20\)

\(\Leftrightarrow7x=14\)

\(\Leftrightarrow x=2\)

\(\frac{x}{-2}=-\frac{8}{x}\)

\(\Leftrightarrow x^2=16\)

\(\Leftrightarrow x=\pm4\)

\(-\frac{2}{x}=\frac{y}{3}\)

\(\Leftrightarrow xy=-6\)

\(\Leftrightarrow x;y\inƯ\left(-6\right)=\left\{\pm1;\pm2;\pm3;\pm6\right\}\)

Xét bảng

x	1	-1	2	-2	3	-3	6	-1
y	-6	6	-3	3	-2	2	-1	6

Vậy.................

\(\frac{2x-9}{240}=\frac{39}{80}\)

\(\Leftrightarrow2x-9=\frac{240.39}{80}\)

\(\Leftrightarrow2x-9=117\)

\(\Leftrightarrow2x=126\)

\(\Leftrightarrow x=63\)