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Миаир
@Миаир
June 2022
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-2cos^2x+7cosx-5>=0
Решить неравенство
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nKrynka
Решение
-2cos^2x+7cosx-5≥0
2cos²x - 7cosx + 5 ≤ 0
cosx = t, I t I ≤ 1
2t² - 7t + 5 = 0
D = 49 - 4*2*5 = 9
t₁ = (7 - 3)/4
t₁ = 1
t₂ = (7 + 3)/4
t₂ = 2,5 , 2,5 не удовлетворяет условию: I t I ≤ 1
cosx = 1
x = 2πk, k∈Z
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Answers & Comments
-2cos^2x+7cosx-5≥0
2cos²x - 7cosx + 5 ≤ 0
cosx = t, I t I ≤ 1
2t² - 7t + 5 = 0
D = 49 - 4*2*5 = 9
t₁ = (7 - 3)/4
t₁ = 1
t₂ = (7 + 3)/4
t₂ = 2,5 , 2,5 не удовлетворяет условию: I t I ≤ 1
cosx = 1
x = 2πk, k∈Z