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deniskaizmailo
@deniskaizmailo
July 2022
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9tg^4x=6tg^2x-1 [-3п/2;0]
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nKrynka
9tg^4x=6tg^2x-1 [-3п/2;0]
9tg^4x - 6tg^2x + 1 = 0
tg
²x = z
9z² - 6z + 1 = 0
D = 36 - 4*9*1 = 0
z
₁ = 6/18
z₁ = 1/3
tg
²x = 1/3
1) tgx = - √3
x = - π/6 + πk, k∈Z
2) tgx = 1/√3
x = π/6 + πn, n∈Z не принадлежит промежутку
[-3п/2;0]
Ответ: x = - π/6 + πk, k∈Z
2 votes
Thanks 6
yalisau
откуда 6/18??
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Answers & Comments
9tg^4x - 6tg^2x + 1 = 0
tg²x = z
9z² - 6z + 1 = 0
D = 36 - 4*9*1 = 0
z₁ = 6/18
z₁ = 1/3
tg²x = 1/3
1) tgx = - √3
x = - π/6 + πk, k∈Z
2) tgx = 1/√3
x = π/6 + πn, n∈Z не принадлежит промежутку [-3п/2;0]
Ответ: x = - π/6 + πk, k∈Z