Решите неравенство 96/(5^(2-x^2) - 1)^2-28/(5^(2-x^2)-1)+1>=0

$dfrac{96}{(5^{2-x^2}-1)^2}-dfrac{28}{5^{2-x^2}-1}+1 geq 0 3AMEHA: 5^{2-x^2}-1=t dfrac{96}{t^2}-dfrac{28}{t}+1 geq 0 dfrac{t^2-28t+96}{t^2} geq 0 dfrac{(t-4)(t-24)}{t^2} geq 0$
+ + - +
-----o-------|------|-------> t
0 4 24
t < 0 или 0 < t ≤ 24 или t ≥ 24
$5^{2-x^2}-1 textless 0$ или $0 textless 5^{2-x^2}-1 leq 4$ или $5^{2-x^2}-1 geq 24$
$5^{2-x^2} textless 5^0$ или $5^0 textless 5^{2-x^2} leq 5^1$ или $5^{2-x^2} geq 5^2$
$x^2-2 textgreater 0$ или $0 textless 2-x^2 leq 1$ или $2-x^2 geq 2$
х² > 2 или 1 ≤ х² < 2 или х² ≤ 0
$left[ begin{matrix} x in (-infty; - sqrt{2}) cup ( sqrt{2};+infty) x in (-sqrt{2};-1] cup [1; sqrt{2}) x=0 end{matrix}right$

Ответ: $(-infty; - sqrt{2}) cup (-sqrt{2};-1] cup {0} cup [1; sqrt{2}) cup ( sqrt{2};+infty).$