Log1/3(x-2)+log1/3(12-x)>=-2

Question

Log1/3(x-2)+log1/3(12-x)>=-2

Answer 1

ОДЗ
x-2>0⇒x>2
12-x>0⇒x<12<br>x∈(2;12)
log(1/3)[(x-2)(12-x)]≥-2
(x-2)(12-x)≤9
12x-x²-24+2x-9≤0
x²-14x+33≥0
x1+x2=14 U x1*x2=33
x1=3 U x2=11
x≤3 U x≥11
x∈(2;3] U [11;12)