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July 2022
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[tex]lg100-lg(x^{2})\geq 2lg^{2}(-x)[/tex]
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армения20171
Lg100-lg(x²)≥2lg²(-x)
x²>0;x≠0
-x>0;x<0
ODZ
2-2lglxl≥2lg²(-x)
2-2lg(-x)-2lg²(-x)≥0
2lg²(-x)+2lg(-x)-2≤0
lg(-x)=t
2t²+2t-2≤0
t²+t-1≤0
D=1+4=5
t=(-1±√5)/2
t€[(-1-√5)/2;(-1+√5)/2]
1)lg(-x)≥(-1-√5)/2
-x≥10^(-1-√5)/2
x≤(-10^(-1-√5)/2)
2)lg(-x)≤(-1+√5)/2
-x≤10^(-1+√5)/2
x≥-10^(-1+√5)/2
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Answers & Comments
x²>0;x≠0
-x>0;x<0
ODZ
2-2lglxl≥2lg²(-x)
2-2lg(-x)-2lg²(-x)≥0
2lg²(-x)+2lg(-x)-2≤0
lg(-x)=t
2t²+2t-2≤0
t²+t-1≤0
D=1+4=5
t=(-1±√5)/2
t€[(-1-√5)/2;(-1+√5)/2]
1)lg(-x)≥(-1-√5)/2
-x≥10^(-1-√5)/2
x≤(-10^(-1-√5)/2)
2)lg(-x)≤(-1+√5)/2
-x≤10^(-1+√5)/2
x≥-10^(-1+√5)/2