Question

(log_0,5(x^2))/(log_0,5(1/4x))>=log_0,5(x^2)

Answer 1

ОДЗ x>0
log(0,5)(0,25x)=log(0,5)0,25+log(0,5)x=2+log(0,5)x
log(0,5)x²=2log(0,5)x
log(0,5)x=a
2a/(2+a)-2a≥0
(2a-4a-2a²)/(2+a)≥0
(-2a-2a²)/(2+a)≥0
2a(1+a)/(2+a)≤0
a=0  a=-1  a=-2
            _               +                _                 +
--------------(-2)---------[-1]------------[0]-----------------
a<-2⇒log(0,5)x<-2⇒x>4
-1≤a≤0⇒-1≤log(0,5)x≤0⇒1≤x≤2
Ответ x∈[1;2] U (4;∞)