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dmitrijfrol201
@dmitrijfrol201
August 2021
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Решите неравенство, указав ОДЗ :
[tex] \frac{ (x-2)^{2} (x+4)}{1-x} \geq 0[/tex]
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m11m
Verified answer
ОДЗ: х≠1
(x-2)²(x+4)(1-x)≥0
-(x-2)²(x+4)(x-1)≥0
(x-2)²(x+4)(x-1)≤0
x=2 x=-4 x=1
+ - + +
---------
-4 ---------------
1 -------------
2
--------------
\\\\\\\\\\\\\\\\
x∈(-∞; -4) x= -5 + - - | +
x∈(-4; 1) x=0 + + - | -
x∈(1; 2) x=1.5 + + + | +
x∈(2; +∞) x=3 + + + | +
x∈[ -4; 1)U{2}
Ответ: [-4; 1)U{2}.
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Answers & Comments
Verified answer
ОДЗ: х≠1(x-2)²(x+4)(1-x)≥0
-(x-2)²(x+4)(x-1)≥0
(x-2)²(x+4)(x-1)≤0
x=2 x=-4 x=1
+ - + +
--------- -4 --------------- 1 ------------- 2 --------------
\\\\\\\\\\\\\\\\
x∈(-∞; -4) x= -5 + - - | +
x∈(-4; 1) x=0 + + - | -
x∈(1; 2) x=1.5 + + + | +
x∈(2; +∞) x=3 + + + | +
x∈[ -4; 1)U{2}
Ответ: [-4; 1)U{2}.