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Katlen
@Katlen
July 2022
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sedinalana
Verified answer
6
(9x²+12x+4)/(x-6)>0
(3x+2)²/(x-6)>0
x=-2/3 x=6
_ _ +
--------------(-2/3)------------------(6)-------------------
x∈(6;∞)
7
(x+2)(x-3)(x-4)/(x-2)²>0
x=-2 x=3 x=4 x=2
_ + + _ +
------------(-2)--------------(2)-------------(3)----------------(4)---------------
x∈(-2;2) U (2;3) U (4;∞)
8
(x-3)^10(x-1)^9x^4(x+2)≤0
x=3 x=1 x=0 x=-2
+ _ _ + +
-----------[-2]------------[0]------------[1]----------------[3]--------------------
x∈[-2;1] U {3}
9
(x²-x+3)(6x+1)^5>0
x²-x+3=0
D=1-12=-11<0при любом х выражение больше 0⇒
(6x+1)^5>0
x>-1/6
x(-1/6;∞)
10
(x^4-8x²-9)/(x³-1)<0
x^4-8x²-9=0
x²=a
a²-8a-9=0
a1+a2=8 U a1*a2=-9
a1=-1 ( a2=9
(x²+1)(x²-9)=0
(x²+1)(x-3)(x+3)=0
x²+1>0 при любом х
x=3 x=-3
x³-1=0⇒x³=1⇒x=1
_ + _ +
--------------(-3)-------------(1)--------------(3)-----------------
x∈(-∞;-3) U (1;3)
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Answers & Comments
Verified answer
6(9x²+12x+4)/(x-6)>0
(3x+2)²/(x-6)>0
x=-2/3 x=6
_ _ +
--------------(-2/3)------------------(6)-------------------
x∈(6;∞)
7
(x+2)(x-3)(x-4)/(x-2)²>0
x=-2 x=3 x=4 x=2
_ + + _ +
------------(-2)--------------(2)-------------(3)----------------(4)---------------
x∈(-2;2) U (2;3) U (4;∞)
8
(x-3)^10(x-1)^9x^4(x+2)≤0
x=3 x=1 x=0 x=-2
+ _ _ + +
-----------[-2]------------[0]------------[1]----------------[3]--------------------
x∈[-2;1] U {3}
9
(x²-x+3)(6x+1)^5>0
x²-x+3=0
D=1-12=-11<0при любом х выражение больше 0⇒
(6x+1)^5>0
x>-1/6
x(-1/6;∞)
10
(x^4-8x²-9)/(x³-1)<0
x^4-8x²-9=0
x²=a
a²-8a-9=0
a1+a2=8 U a1*a2=-9
a1=-1 ( a2=9
(x²+1)(x²-9)=0
(x²+1)(x-3)(x+3)=0
x²+1>0 при любом х
x=3 x=-3
x³-1=0⇒x³=1⇒x=1
_ + _ +
--------------(-3)-------------(1)--------------(3)-----------------
x∈(-∞;-3) U (1;3)