Question

Rezolvati in R ecuatia:
$3 - \sqrt[3]{ {x}^{2} + x + 2} = 1$
va rog dau funda!​

Answer 1

$\it 3-\sqrt[3]{\it x^2+x+2}=1 \Rightarrow 3=1+\sqrt[3]{x^2+x+2} \Rightarrow 1+\sqrt[3]{\it x^2+x+2}=3|_{-1} \Rightarrow\\\ \\\ \Rightarrow \sqrt[3]{\it x^2+x+2}=2 \Rightarrow (\sqrt[3]{\it x^2+x+2})^3=2^3 \Rightarrow x^2+x+2=8|_{-8} \Rightarrow\\\ \\\ \Rightarrow x^2+x-6=0 \Rightarrow x^2+3x-2x-6=0 \Rightarrow x(x+3)-2(x+3)=6 \Rightarrow\\ \\ \\ (x+3)(x-2)=0 \Rightarrow \begin{cases}\it x+3=0 \Rightarrow x_1=-3\\ \\ \it x-2=0\ \ \Rightarrow\ x_2=2\end{cases}$