Question

Tìm x, y, z, t ∈ Z biết:

a, \(\dfrac{5}{x}=\dfrac{-10}{12}\)       b, \(\dfrac{4}{-6}=\dfrac{x+3}{9}\)            c, \(\dfrac{x-1}{25}=\dfrac{4}{x-1}\)    d, \(\dfrac{x+1}{y}=\dfrac{-3}{5}\)

e, \(\dfrac{-12}{6}=\dfrac{x}{5}=\dfrac{-y}{3}=\dfrac{Z}{-17}=\dfrac{-t}{-9}\)

h, \(\dfrac{-24}{-6}=\dfrac{x}{3}=\dfrac{4}{y^2}=\dfrac{Z^3}{-2}\)

Answer 1

a) \(\dfrac{5}{x}=\dfrac{-10}{12}.\Rightarrow x=-6.\)

b) \(\dfrac{4}{-6}=\dfrac{x+3}{9}.\Rightarrow x+3=-6.\Leftrightarrow x=-9.\)

c) \(\dfrac{x-1}{25}=\dfrac{4}{x-1}.\left(đk:x\ne1\right).\Leftrightarrow\dfrac{x-1}{25}-\dfrac{4}{x-1}=0.\)

\(\Leftrightarrow\dfrac{x^2-2x+1-100}{25\left(x-1\right)}=0.\Leftrightarrow x^2-2x-99=0.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=11.\\x=-9.\end{matrix}\right.\) \(\left(TM\right).\)