Question

Sa se rezolve in R ecuația

Answer 1

$\it \left(\dfrac{1}{5}\right)^{3x^2+x-13} =125 \Leftrightarrow \left(\dfrac{1}{5}\right)^{3x^2+x-13} = \left(\dfrac{1}{5}\right)^{-3} \Leftrightarrow 3x^2+x-13=-3\Leftrightarrow\\ \\ \\ \Leftrightarrow 3x^2+x-10=0 \Leftrightarrow 3x^2+6x-5x-10=0\Leftrightarrow3x(x+2) -5(x+2)=0\Leftrightarrow\\ \\ \Leftrightarrow (x+2)(3x-5) =0 \Leftrightarrow \begin{cases} \it x+2=0 \Rightarrow x_1 = -2\\ \\ \it 3x-5=0 \Rightarrow 3x=5 \Rightarrow x_2=\dfrac{5}{3}\end{cases}$