ДАЮ 99 БАЛЛОВ! СРОЧНО! Решите неравенство Каждое подробно. 1. (x-3) (x+1) (x+4)<0 2. 1/3...

1. (x-3) (x+1) (x+4)<0 x=3 x=-1 x=-4
 _ + _ +
---------------(-4)-----------(-1)-------------(3)-------------------
x∈(-∞;-4) U (-1;3)
2. 1/3 x^3 - 3х <= 0 1/3x(x²-9)≤0
1/3x(x-3)(x+3)≤0
x=0 x=3 x=-3
_ + _ +
---------------[-3]-----------[0]-------------[3]-------------------
x∈(-∞;-3] U [0;3]
3. (x^2+6x+9) (x^2-1) <= 0 (x+3)²(x-1)(x+1)≤0
x=-3 x=1 x=-1
+ + _ +
---------------[-3]-----------[-1]-------------[1]--------------
x∈[-1;1] U {-3}
4. (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;∞)
5. (x^2-x+3) (6x+1)^5 > 0
x²-x+3=0
D=1-12=-11<0⇒x²-x+3>0 при любом х⇒(6x+1)^5>0
6x+1>0⇒6x>-1⇒x>-1/6
x∈(-1/6;∞)
6. (3x-1) (x-2) (x+1) > 0
x=1/3 x=2 x=-1
_ + _ +
------------(-1)--------------(1/3)-------------(2)-------------------
x∈(-1;1/3) U (2;∞)
7. (x^2-7x+12) (x^2-4) >= 0
x²-7x+12=0⇒x1+x2=7 U x1*x2=12⇒x1=3 U x2=4
x²-4=0⇒x²=4⇒x=-2 U x=2
 + _ + _ +
---------------[-2]-----------[2]-------------[3]------------[4]----------
x∈(-∞;-2] U [2;3] U [4;∞)
8.( 9x^2+12x+4) / (x-6 )>= 0
(3x+2)²(x-6)≤0
x=-2/3 x=6
 _ _ +
-----------[2/3]------------[6]-------------
x∈[6;∞) U {2/3}
9. (x-3)^10 (x-1)^9 x^4(x+2)<=0 x=3 x=1 x=0 x=-2
 + _ _ + +
----------[-2]---------[0]---------[1]---------[3]-----------
x∈[-2;1] U {3}
10.( x^4-8x^2-9) / (x^3-1)
x^4-8x²-9=0
x²=a
a²-8a-9=0⇒a1+a2=8 U a1*a2=-9⇒a1=-1 U a2=9
(x²+1)(x²-9)/(x³-1)<0 (x²+1)(x-3)(x+3)/(x-1)(x²+x+1)<0 x²+1>0 при любом х и x²+x+1>0 при любом х⇒
(x-3)(x+3)/(x-1)<0 x=3 x=-3 x=1
_ + _ +
---------------(-3)-----------(1)-------------(3)------------------
x∈(-∞;-3) U (1;3)