Լուծեք անհավասարումը.
107. ա) (2x – 1) (3x + 5) < 0
(2x – 1) (3x + 5) = 0
2x – 1 = 0 |2x = 1 |x = 0,5
3x + 5 = 0 |3x = –5 |x = –5/3
x∈ (–5/3 ; 0,5)
բ) (1,2x – 0,75) (7x – 1) < 0
(1,2x – 0,75) (7x – 1) = 0
1,2x – 0,75 = 0 |1,2x = 0,75 |x = 0,625
7x – 1 = 0 |7x = 1 |x = 1/7
x∈ (1/7 ; 0,625)
գ) (4x + 3) (5x + 2) > 0
(4x + 3) (5x + 2) = 0
4x + 3 = 0 |4x = –3 |x = –0,75
5x + 2 = 0 |5x = –2 |x = –0,4
x∈ (–∞ ; –0,4) ∪ (–0,7 ; +∞)
դ) (1 1/3x + 1/12) (0,7x + 4) > 0
(1 1/3x + 1/12) (0,7x + 4) = 0
1 1/3x + 1/12 = 0 |4/3x = –1/12 |x = –3/48
0,7x + 4 = 0 |0,7x = –4 |x = –5,7
x∈ (–∞ ; –3/48) ∪ (–5,7 ; +∞)
108.
ա) x² – x > 0
x² – x = 0
x(x – 1) = 0
x = 0 |x = 0
x – 1 = 0 |x = 1
x∈ (–∞ ; 0) ∪ (1 ; +∞)
բ) x² + x < 0
x² + x = 0
x(x + 1) = 0
x = 0 |x = 0
x + 1 = 0 |x = –1
x∈ (–1 ; 0)
գ) 5x² – x < 0
5x² – x = 0
x(5x – 1) = 0
x = 0 |x = 0
5x – 1 = 0 |5x = 1 x = 1/5 x = 0,2
x∈ (0 ; 0,2)
դ) 3x² + x > 0
3x² + x = 0
x(3x + 1) = 0
x = 0 |x = 0
3x + 1 = 0 |x = –1/3
x∈ (–∞ ; –1/3) ∪ (0 ; +∞)
ե) 4x² + 7x > 0
4x² + 7x = 0
x(4x + 7) = 0
x = 0 |x = 0
4x + 7 = 0 |x = –7/4
x∈ (0 ; +∞) ∪ (–∞ ; –1,75)
զ) 3x – 2x² < 0
3x – 2x² = 0
x(3 – 2x) = 0
x = 0 |x = 0
3 – 2x = 0 |x = 2/3
x∈ (0 ; 2/3)
109.
ա) x² – 4 > 0
x² – 4 = 0
x² – 2² = (x – 2)(x + 2) = 0
x – 2 = 0 |x = 2
x + 2 = 0 |x = –2
x∈ (–∞ ; –2) ∪ (2 ; +∞)
բ) x² – 9 < 0
x² – 9 = 0
x² – 3² = (x – 3)(x + 3) = 0
x – 3 = 0 |x = 3
x + 3 = 0 |x = –3
x∈ (–3 ; 3)
գ) x² – 100 < 0
x² – 100 = 0
x² – 10² = (x – 10)(x + 10) = 0
x – 10 = 0 |x = 10
x + 10 = 0 |x = –10
x∈ (–10 ; 10)
դ) 1 – x² > 0
1 – x² = 0
1 – x² = (1 – x)(1 + x) = 0
1 – x = 0 |x = 1
1 + x = 0 |x = –1
x∈ (–∞ ; –1) ∪ (1 ; +∞)
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