Question

\(\dfrac{\left(-5\right)^{9x^2+1}}{25}=-125\)

Answer 1

\(\dfrac{\left(-5\right)^{9x^2+1}}{25}=-125\)

\(\Leftrightarrow\left(-5\right)^{9x^2+1}=-5^5\)

\(\Leftrightarrow9x^2=4\)

hay \(x\in\left\{\dfrac{2}{3};-\dfrac{2}{3}\right\}\)

Answer 2

\(\Leftrightarrow\left(-5\right)^{9x^2+1}=-125\cdot25=\left(-5\right)^5\\ \Leftrightarrow9x^2+1=5\Leftrightarrow x^2=\dfrac{4}{9}\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-\dfrac{2}{3}\end{matrix}\right.\)

Answer 3

<=> \(\left(-5\right)^{9x^2+1}=-3125\)

<=> \(\left(-5\right)^{9x^2+1}=\left(-5\right)^5\)

<=> 9x² + 1 = 5

<=> 9x² + 1 - 5 = 0

<=> 9x² - 4 = 0

<=> (3x - 2)(3x + 2) = 0

<=> \(\left[{}\begin{matrix}3x-2=0\\3x+2=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=\dfrac{-2}{3}\end{matrix}\right.\)