ПОМОГИТЕ!Решить неравенство:
1) 1/3х(х+1) ≤ (х-1)²
2)1/3х - 4/9 ≥ х(х-1)
3)2х-2,5 > х(х-1)
1) 1/3х(х+1) ≤ (х-1)²
2)1/3х - 4/9 ≥ х(х-1)
3)2х-2,5 > х(х-1)
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1) √3/ 3-x² < 2/ √3-x
2/(√3-x)-√3/(√3-x)(√3+x)>0
(2√3+2x-√3)/(√3-x)(√3+x)>0
(2x+√3)/(√3-x)(√3+x)>0
x=-√3/2 x=√3 x=-√3
+ _ + _
---------------(-√3)------------------[-√3/2]----------(√3)--------------------
x∈(-∞;-√3) U [-√3/2;√3)
2)3/ x²-1 - 1/2 < 3/ 2x-2
3/2(x-1)-3/(x-1)(x+1)+1/2>0
(3x+3-6+x²-1)/2(x-1)(x+1)>0
(x²+3x-4)/2(x-1)(x+1)>0
x²+3x-4=0⇒x1+x2=-3 U x1*x2=-4⇒x1=-4 U x2=1
(x+4)(x-1)/2(x-1)(x+1)>0
(x+4)/2(x+1)>0
x=-4 x=-1
+ _ + _
-------------(-4)----------------(-1)---------------(1)---------------
x∈(-∞-4) U (-1;1) U (1;∞)