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nas1234987
@nas1234987
August 2022
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Помогите решить неравенство
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sedinalana
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ОДЗ x>0 U x≠1/2
Перейдем к основанию 2
-3/(1+log(2)x)≥6+log(2)x-1
5+log(2)x+3/(1+log(2)x)≤0
log(2)x=a
5+a+3/(1+a)≤0
(5+5a+a+a²+3)/(1+a)≤0
(a²+6a+8)/(1+a)≤0
a²+6a+8=0
a1+a2=-6 U a1*a2=8
a1=-4 U a2=-2
1+a=0⇒a=-1
_ + _ +
---------------[-4]---------------[-2]--------------(-1)----------------
a≤-4⇒log(2)x≤-4⇒x≤1/16
-2≤a<-1⇒-2≤log(2)x<-1⇒1/4≤x<1/2
x∈(0;1/16] U [1/4;1/2)
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Verified answer
ОДЗ x>0 U x≠1/2Перейдем к основанию 2
-3/(1+log(2)x)≥6+log(2)x-1
5+log(2)x+3/(1+log(2)x)≤0
log(2)x=a
5+a+3/(1+a)≤0
(5+5a+a+a²+3)/(1+a)≤0
(a²+6a+8)/(1+a)≤0
a²+6a+8=0
a1+a2=-6 U a1*a2=8
a1=-4 U a2=-2
1+a=0⇒a=-1
_ + _ +
---------------[-4]---------------[-2]--------------(-1)----------------
a≤-4⇒log(2)x≤-4⇒x≤1/16
-2≤a<-1⇒-2≤log(2)x<-1⇒1/4≤x<1/2
x∈(0;1/16] U [1/4;1/2)