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RollingStone
@RollingStone
July 2022
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Решить неравенство, 10-ый класс (см. вложение) = 35 баллов
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juleeekk
ОДЗ
5^(x+1)-25^x>0
5^x=a
5a-a²>0
a(5-a)>0
a=0 a=5
0<a<5⇒0<5^x<5⇒x<1
x∈(-∞;1)
5^(x+1)-25^x≥6
5^x=a
a²-5a+6≤0
a1+a2=5 U a1*a2=6⇒a1=2 U a2=3
2≤a≤3⇒2≤5^x≤3⇒log(5)2≤x≤log(5)3
Ответ x∈[log(5)2;log(5)3]
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sedinalana
Verified answer
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Answers & Comments
5^(x+1)-25^x>0
5^x=a
5a-a²>0
a(5-a)>0
a=0 a=5
0<a<5⇒0<5^x<5⇒x<1
x∈(-∞;1)
5^(x+1)-25^x≥6
5^x=a
a²-5a+6≤0
a1+a2=5 U a1*a2=6⇒a1=2 U a2=3
2≤a≤3⇒2≤5^x≤3⇒log(5)2≤x≤log(5)3
Ответ x∈[log(5)2;log(5)3]
Verified answer
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