Question

a)( \(\dfrac{-3}{4}\))\(^{^{ }3x-1}\)=\(\dfrac{256}{81}\)

b) (x-7)\(^{x+1}\) - (x-7)\(^{x+11}\) = 0

c)(x - \(\dfrac{1}{2}\))\(^2\) + (y + \(\dfrac{1}{2}\))\(^2\) =0

Answer 1

a: \(\left(-\dfrac{3}{4}\right)^{3x-1}=\dfrac{256}{81}\)

\(\Leftrightarrow\left(-\dfrac{3}{4}\right)^{3x-1}=\left(-\dfrac{3}{4}\right)^{-4}\)

=>3x-1=-4

=>3x=-3

hay x=-1

b: \(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)

\(\Leftrightarrow\left(x-7\right)^{x+1}\left[1-\left(x-7\right)^{10}\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x-7=-1\\x-7=1\end{matrix}\right.\Leftrightarrow x\in\left\{7;6;8\right\}\)

c: \(\left(x-\dfrac{1}{2}\right)^2+\left(y+\dfrac{1}{2}\right)^2=0\)

=>x-1/2=0 và y+1/2=0

=>x=1/2 và y=-1/2