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klera1111
@klera1111
August 2022
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найти область определения функции
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армения20171
(8-2х)/(х+3)-2/х>0
(х(8-2х)-2(х+3))/х(х+3)>0
(8х-2х²-2х-6)/х(х+3)>0
-2(х²-3х+3)/х(х+3)>0
(х²-3х+3)/х(х+3)<0
х²-3х+3=х²-2*3/2*х+9/4-9/4+3=
(х-3/2)²+3/4 всегда положительный
х(х+3)<0
х€(-3;0)
ответ (-3;0)
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Answers & Comments
(х(8-2х)-2(х+3))/х(х+3)>0
(8х-2х²-2х-6)/х(х+3)>0
-2(х²-3х+3)/х(х+3)>0
(х²-3х+3)/х(х+3)<0
х²-3х+3=х²-2*3/2*х+9/4-9/4+3=
(х-3/2)²+3/4 всегда положительный
х(х+3)<0
х€(-3;0)
ответ (-3;0)