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kub999
@kub999
August 2022
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(4-8х)(х+9) > (2х-1)/7. Решите неравенство.
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EmiliedeRavin
(4-8х)(х+9) > (2х-1)/7 I * 7
7*(4-8х)(х+9) >2x-1
7*(
4х
+36-8х²-
72х
)>2x-1
7*(-8х²-68х+36)>2x-1
-56х²-476х+252>2x-1
-56х²-
476х
+
252
-
2х
+
1
>0
-56х²-478х+253>0 I:(-1)
56x²+478x-253
<0
D=228484+56672=285156=534²
x1=(-478+534)/112=0,5
x2=(-478-534)/112=-1012/112=-506/56=-253/28=-9 целых 1/28
+ +
-9 целых 1/28 ////////////////////// 0,5
-
Ответ: х ∈( -9 целых 1/28 ; 0,5 )
1 votes
Thanks 1
kub999
7*(4-8х)(х+9) >2x-1;
kub999
7*(4-8х)(х+9) >2x-1; ((28-56х)(х+9)-(2х-1))> 0. Что будет если вынести 2х-1 за скобку
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Answers & Comments
7*(4-8х)(х+9) >2x-1
7*(4х+36-8х²-72х)>2x-1
7*(-8х²-68х+36)>2x-1
-56х²-476х+252>2x-1
-56х²-476х+252-2х+1>0
-56х²-478х+253>0 I:(-1)
56x²+478x-253<0
D=228484+56672=285156=534²
x1=(-478+534)/112=0,5
x2=(-478-534)/112=-1012/112=-506/56=-253/28=-9 целых 1/28
+ +
-9 целых 1/28 ////////////////////// 0,5
-
Ответ: х ∈( -9 целых 1/28 ; 0,5 )