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Irinasharova
@Irinasharova
August 2022
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помогите решить уравнение 5tg x - 12ctg x + 11 = 0
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Dимасuk
Verified answer
5tgx - 12/tgx + 11 = 0
5tg²x + 11tgx - 12 = 0 (tgx ≠ 0)
Пусть t = tgx.
5t² + 11t - 12 = 0
D = 121 + 5•12•4 = 361 = 19²
t1 = (-11 + 19)/10 = 8/10 = 4/5
t2 = (-11 - 19)/10 = -30/10 = -3
Обратная замена:
tgx = 4/5
x = arctg(4/5) + πn, n ∈ Z
tgx = -3
x = arctg(-3) + πn, n ∈ Z.
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Answers & Comments
Verified answer
5tgx - 12/tgx + 11 = 05tg²x + 11tgx - 12 = 0 (tgx ≠ 0)
Пусть t = tgx.
5t² + 11t - 12 = 0
D = 121 + 5•12•4 = 361 = 19²
t1 = (-11 + 19)/10 = 8/10 = 4/5
t2 = (-11 - 19)/10 = -30/10 = -3
Обратная замена:
tgx = 4/5
x = arctg(4/5) + πn, n ∈ Z
tgx = -3
x = arctg(-3) + πn, n ∈ Z.