Question

Rezolvă, în mulțimea numerelor reale, următoarele ecuații:​

Answer 1

$\it a) \ \ 3x^2-6x=0|_{:3} \Rightarrow x^2-2x=0 \Rightarrow x(x-2)=0 \Rightarrow \begin{cases}\it x_1=0\\ \\ \it x-2=0 \Rightarrow x_2=2\end{cases}\\ \\ \\ b) \ \ 6x^2-5x=0|_{:6} \Rightarrow x^2-\dfrac{5}{6}x=0 \Rightarrow x(x-\dfrac{5}{6})=0 \Rightarrow \begin{cases}\it x_1=0\\ \\ \it x_2=\dfrac{5}{6}\end{cases}$

$\it e)\ 36x^2-25=0 \Rightarrow 36x^2=25 \Rightarrow x^2=\dfrac{25}{36} \Rightarrow \sqrt{x^2}=\sqrt{\dfrac{25}{36}} \Rightarrow \\ \\ \Rightarrow |x|=\dfrac{5}{6} \Rightarrow x=\pm\dfrac{5}{6}\\ \\ \\ f)\ 2x^2-18=0 \Rightarrow 2x^2=18|_{:2} \Rightarrow x^2=9 \Rightarrow \sqrt{x^2}=\sqrt9 \Rightarrow \\ \\ \Rightarrow |x|=3 \Rightarrow x=\pm3\\ \\ g)\ x^2-50=0 \Rightarrow x^2=50 \Rightarrow \sqrt{x^2}=\sqrt{50} \Rightarrow |x|=\sqrt{25\cdot2} \Rightarrow x=\pm5\sqrt2$