Question

log√2 (6-x ^(2)) > 2

Answer 1

ОДЗ : 6 - x² > 0
x² - 6 < 0
(x - √6)(x + √6) < 0
x ∈ (- √6 ; √6)

$log _{ \sqrt{2} }(6- x^{2} )\ \textgreater \ 2\\\\6- x^{2} \ \textgreater \ ( \sqrt{2}) ^{2} \\\\ 6- x^{2} \ \textgreater \ 2\\\\4- x^{2}\ \textgreater \ 0\\\\ x^{2} -4\ \textless \ 0$
$(x-2)(x+2)\ \textless \ 0$
          +                      -                       +
___________₀___________₀____________
                     -2                      2
x ∈ (- 2 ; 2)