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nik5127
@nik5127
August 2022
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Решите пожалуйста неравенство!)
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sedinalana
Verified answer
ОДЗ
5^x≠1⇒x≠0 U 5^x≠3⇒x≠log(5)3
5^x=a
2/(a-1) +(a-2)/(a-3)≥2
2-2/(a-1)-(a-2)/(a-3)≤0
(2a²-8a+6-2a+6-a²+2a+a-2)/(a-1)(a-3)≤0
(a²-7a+10)/(a-1)(a-3)≤0
a²-7a+10=0
a1+a2=7 U a1*a2=10⇒a1=2 U a2=5
a-1=0⇒a=1
a-3=0⇒a=3
+ _ + _ +
------------(1)-----------------[2]-------------(3)---------------[5]----------------
1<a≤2⇒1<5^x≤2⇒0<x≤log(5)2
3<a≤5⇒3<5^x≤5⇒log(5)3<x≤1
Ответ x∈(0;log(5)2] U (log(5)3;1]
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Answers & Comments
Verified answer
ОДЗ5^x≠1⇒x≠0 U 5^x≠3⇒x≠log(5)3
5^x=a
2/(a-1) +(a-2)/(a-3)≥2
2-2/(a-1)-(a-2)/(a-3)≤0
(2a²-8a+6-2a+6-a²+2a+a-2)/(a-1)(a-3)≤0
(a²-7a+10)/(a-1)(a-3)≤0
a²-7a+10=0
a1+a2=7 U a1*a2=10⇒a1=2 U a2=5
a-1=0⇒a=1
a-3=0⇒a=3
+ _ + _ +
------------(1)-----------------[2]-------------(3)---------------[5]----------------
1<a≤2⇒1<5^x≤2⇒0<x≤log(5)2
3<a≤5⇒3<5^x≤5⇒log(5)3<x≤1
Ответ x∈(0;log(5)2] U (log(5)3;1]