Question

Решить неравенство (x^2-x-1)(x^2-x-7)<-5

Answer 1

x²-x-1=a
a(a-6)+5<0
a²-6a+5<0
a1+a2=6 U a1*a2=5
a1=1 U a2=5
1<a<5
{x²-x-1>1  (1)
{x²-x-1<5  (2)
(1) x²-x-2>0
x1+x2=1 U x1*x2=-2
x1=-1 U x2=2
x<-1 U x>2
(2) x²-x-6<0
x1+x2=1 U x1*x2=-6
x1=-2 U x2=3
-2<x<3
x∈(-2;-1) U (2;3)