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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Verified answer
1) 1/3х(х+1) ≤ (х-1)²1/3*x(x+1)-(x-1)(x+1)≤0
(x-1)*(1/3*x-x-1)≤0
(x-1)(2/3*x+1)≥0
x=1 x=-1,5
x∈(-∞;-1,5] U [1;∞)
2)1/3х - 4/9 ≥ х(х-1)
x²-x-1/3*x+4/9≤0
x²-4/3*x+4/9≤0
9x²-12x+4≤0
(3x-2)²≤0
3x=2
x=2/3
3)2х-2,5 > х(х-1)
x²-x-2x+2,5<0
x²-3x+2,5<0
D=9-10=-1<0
нет решения