Lg(x^2-2)=lg x. Решите пожалуйста!!

Решите задачу:

$lg(x^2-2)=lgx\\ \left \{ {{x^2-2\ \textgreater \ 0} \atop {x\ \textgreater \ 0}} \right. =\ \textgreater \ \left \{ {{(x- \sqrt{2})(x+ \sqrt{2})\ \textgreater \ 0 } \atop {x\ \textgreater \ 0}} \right. =\ \textgreater \ \left \{ {{x\ \textless \ - \sqrt{2},\; \; x\ \textgreater \ \sqrt{2} } \atop {x\ \textgreater \ 0}} \right. =\ \textgreater \ x\ \textgreater \ \sqrt{2}\\\\x^2-2=x\\x^2-x-2=0\\(x+1)(x-2)=0\\x_1=-1\; \; (\ \textless \ 0)\\x_2=2\; \; (\ \textgreater \ \sqrt{2}) \\\\x=2$