Question

Решите уравнение $27^{tg^{2} x} +81*27^{-tg^{2}x} =30$

Answer 1

27^tg²x=a
a+81/a-30=0
a²-30a+81=0
a1+a2=30 U a1*a2=81
a1=3⇒27^tg²x=3⇒3^3tg²x=3⇒3tg²x=1⇒tg²x=1/3
tgx=-1/√3⇒x=-π/6+πn,n∈z
tgx=1/√3⇒x=π/6+πn,n∈z
a2=27⇒27^tg²x=27⇒tg²x=1
tgx=-1⇒x=-π/4+πn,n∈z
tgx=1⇒x=π/4+πn,n∈z