This is LaTeX code:
[latex]
(\alpha ^{2} x_1^2 - \alpha^2 x_2 ^2)\alpha^2 x_3^2 \in \mathbb{R} \Leftrightarrow \alpha^4 (x_1^2 - x_2 ^2)x_3^2 \in \mathbb{R}
[/latex]