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Ханма
@Ханма
August 2022
1
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Срочно,пожалуйста!Решите методом интервалов неравенство:а)(х+4)(х-1)меньше или равно 0;б)х+6/х-2 больше 4
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m11m
Verified answer
A)
(x+4)(x-1)≤0
x=-4 x=1
+ - +
--------
-4 ----------- 1
-------------
\\\\\\\\\\\\\\\
x∈[-4; 1]
Ответ: [-4; 1]
b)
ОДЗ: x-2≠0
x≠2
[(x+6)/(x-2)] -4>0
[x+6-4(x-2)] / [x-2] >0
[x+6-4x+8] / [x-2] >0
[-3x+14] / [x-2]>0
(-3x+14)(x-2)>0
-3(x-¹⁴/₃)(x-2)>0
(x-4 ²/₃)(x-2)<0
x=4 ²/₃ x=2
+ - +
--------- 2 ------------ 4 ²/₃ ------------
\\\\\\\\\\\\\
x∈(2; 4 ²/₃)
Ответ(2; 4 ²/₃).
1 votes
Thanks 1
Ханма
Спасибо большое.Можете помочь с еще одним заданием?
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Answers & Comments
Verified answer
A)(x+4)(x-1)≤0
x=-4 x=1
+ - +
-------- -4 ----------- 1 -------------
\\\\\\\\\\\\\\\
x∈[-4; 1]
Ответ: [-4; 1]
b)
ОДЗ: x-2≠0
x≠2
[(x+6)/(x-2)] -4>0
[x+6-4(x-2)] / [x-2] >0
[x+6-4x+8] / [x-2] >0
[-3x+14] / [x-2]>0
(-3x+14)(x-2)>0
-3(x-¹⁴/₃)(x-2)>0
(x-4 ²/₃)(x-2)<0
x=4 ²/₃ x=2
+ - +
--------- 2 ------------ 4 ²/₃ ------------
\\\\\\\\\\\\\
x∈(2; 4 ²/₃)
Ответ(2; 4 ²/₃).