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meme9
@meme9
August 2021
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Очень прошу , решите неравенства с 1 по 5
даю высокий бал
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flsh
1.
x ∈ [0; 3)
2.
(3x + 1)³ > (7x + 1)²
27x³ + 27x² + 9x + 1 > 49x² + 14x + 1
27x³ - 22x² - 5x > 0
x(27x² - 22x - 5) > 0
x(x - 1)(27x + 5) > 0
x ∈ (-5/27; 0) ∪ (1; +∞)
3.
x ∈(2; 4) ∪ (4; 6)
4.
x ∈(-π/3; 1)
5.
log₄x·(log₄x - 2) < 0
Замена: log₄x = t
t·(t - 2) < 0
t ∈(0; 2)
x ∈(1; 16)
6.
√2·tg x·ctg x < 2· cos x
x ∈(-π/4 + 2πn; 2πn) ∪ (2πn; π/4 + 2πn), n ∈ Z
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Answers & Comments
x ∈ [0; 3)
2.
(3x + 1)³ > (7x + 1)²
27x³ + 27x² + 9x + 1 > 49x² + 14x + 1
27x³ - 22x² - 5x > 0
x(27x² - 22x - 5) > 0
x(x - 1)(27x + 5) > 0
x ∈ (-5/27; 0) ∪ (1; +∞)
3.
x ∈(2; 4) ∪ (4; 6)
4.
x ∈(-π/3; 1)
5.
log₄x·(log₄x - 2) < 0
Замена: log₄x = t
t·(t - 2) < 0
t ∈(0; 2)
x ∈(1; 16)
6.
√2·tg x·ctg x < 2· cos x
x ∈(-π/4 + 2πn; 2πn) ∪ (2πn; π/4 + 2πn), n ∈ Z