a) áp dụng tính chất dãy tỉ số = nhau ta có:
y-x/2-3 =21/-1 =-21
x= -21.2=-42
y=-21 .3=-63
a) Ta có: \(\dfrac{x}{2}=\dfrac{y}{5}\)
và \(y-x=21\)
Áp dụng tính chất dãy tỷ số bằng nhau ta có:
\(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{y-x}{5-2}=\dfrac{21}{3}=7\\ \Rightarrow\left\{{}\begin{matrix}x=7.2\\y=7.5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=14\\y=35\end{matrix}\right.\)
Vậy...
b) Ta có: \(x:y=3:7\)
\(\Rightarrow\dfrac{x}{3}=\dfrac{y}{7}\)
Và \(x+y=25\)
Áp dụng tính chất dãy tỷ số bằng nhau ta có:
\(\dfrac{x}{3}=\dfrac{y}{7}=\dfrac{x+y}{3+7}=\dfrac{25}{10}=\dfrac{5}{2}\\ \Rightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}.3\\y=\dfrac{5}{2}.7\end{matrix}\right. \Rightarrow\left\{{}\begin{matrix}x=\dfrac{15}{2}\\y=\dfrac{35}{2}\end{matrix}\right.\)
Vậy...
9: Ta có: \(\left(\dfrac{1}{2}x+3\right)^2=36\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x+3=6\\\dfrac{1}{2}x+3=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x=3\\\dfrac{1}{2}x=-9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-18\end{matrix}\right.\)
10: Ta có: \(\left(2x-1\right)^3=-64\)
\(\Leftrightarrow2x-1=-4\)
\(\Leftrightarrow2x=-3\)
hay \(x=-\dfrac{3}{2}\)
11: Ta có: \(3^{x+2}=27^4\)
\(\Leftrightarrow3^{x+2}=3^{12}\)
\(\Leftrightarrow x+2=12\)
hay x=10
12: Ta có: \(x+4x-\dfrac{1}{3}=-\dfrac{1}{6}\)
\(\Leftrightarrow5x=\dfrac{1}{6}\)
hay \(x=\dfrac{1}{30}\)
