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NYE2299
@NYE2299
July 2022
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помогите пожалуйста. показательные уравнения и неравенства
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ВладимирБ
Verified answer
1) (1/3)ˣ = y
y² - 8y -9 = 0
по т. Виета у₁ = -1 и у₂ = 9
(1/3)ˣ = -1
нет решений
(1/3)ˣ = 9
х = -2
2) 8ˣ = 128*2¹/²
2³ˣ =2⁷*2¹/²
3х = 7,5
х =2,5
3) 4ˣ + 2ˣ⁺¹ - 8 > 0
(2ˣ)² + 2ˣ *2 -8 > 0
2ˣ = y
y² +2y -8 > 0 ( корни -4 и 2)
у < - 4 y > 2
2ˣ >2
x > 1
4) 5³ *4²ˣ⁺³ > 1/4 * 2⁻¹/²
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Answers & Comments
Verified answer
1) (1/3)ˣ = yy² - 8y -9 = 0
по т. Виета у₁ = -1 и у₂ = 9
(1/3)ˣ = -1
нет решений
(1/3)ˣ = 9
х = -2
2) 8ˣ = 128*2¹/²
2³ˣ =2⁷*2¹/²
3х = 7,5
х =2,5
3) 4ˣ + 2ˣ⁺¹ - 8 > 0
(2ˣ)² + 2ˣ *2 -8 > 0
2ˣ = y
y² +2y -8 > 0 ( корни -4 и 2)
у < - 4 y > 2
2ˣ >2
x > 1
4) 5³ *4²ˣ⁺³ > 1/4 * 2⁻¹/²