Question

Решите неравенство $-4 leq 3^{x^2-2x-1}-5 leq 4$

Answer 1

-4+5≤3^(x²-2x-1)≤4+5
1≤3^(x²-2x-1)≤9
{x²-2x-1≥0
{x²-2x-1≤2
1)D=4+4=8
x1=(2-2√2)/2=1-√2 U x2=1+√2
x≤1-√2 U x≥1+√2
2)x²-2x-3≤0
x1+x2=2 u x1*x2=-3
x1=-1 u x2=3
-1≤x≤3
x∈[-1;1-√2]