x2–x–2 >0
log1/2(x2–x–2) >–2
log1/2(x2–x–2) >–2·log1/2(1/2)
log1/2(x2–x–2) >log1/2(1/2)–2
log1/2(x2–x–2) >log(1/2)(4)
(1/2)<1 логарифмическая функция убывает
(x2–x–2)< 4
Решаем систему неравенств
{x2–x–2 >0
{x2–x–2 <4
{(x+1)(x–2) >0
{(x+2)(x–3) <0
О т в е т.
(–2;–1) U(2;3)