Помогите решитьtg^2x+3tgx=-2. Created by vson. algebra-ru

Помогите решитьtg^2x+3tgx=-2...

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Tg²x+3tgx=-2
tg²x+3tgx+2=0
Замена: t=tgx
t²+3t+2=0
t₁=-1; t₂=-2 (по теореме Виета)
tgx₁=-1 tgx₂=-2
x₁= -π/4+πn, n∈Z x₂=arctg(-2)+πn,n∈Z
x₂=-arctg2+πn,n∈Z

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mmb1

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tg^2x+3tgx=-2
заметич что это квадратное уравнение относительно tgx=t
t²+3t+2=0
D=9-8=1
t12=(-3+-1)/2=-2 -1
t=-1
tgx=-1
x=-π/4+πN
tgx=-2
x=-arctg (2)+πN

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