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)