Question

Tan^3 x + tan^2 x - 3 tan x - 3 = 0

Answer 1

Ответ: -p/4 +pn,  p/3 +pn,  -p/3 +pn,  n  E  Z

Объяснение: (V-корень обозначен)

tg^2 x(tgx +1) -3(tgx +1)=0,  (tg x+1)(tg^2x-3)=0,

tgx+1=0,  tgx=-1,  x=-p/4 +pn,  n  E  Z,  tg^2 x-3=0,  tg^2 x =3,

tgx=V3,  x=p/3+pn,  tgx= -V3,  x=-p/3 +pn

Answer 2

To solve the equation $\tan^3 x + \tan^2 x - 3\tan x - 3 = 0$, you can substitute $\tan x = t$ to get a cubic equation in $t$:

$t^3 + t^2 - 3t - 3 = 0$

Unfortunately, this cubic equation does not have a simple factorization, so you may need to use numerical methods or special formulas to find its solutions. One common approach is to use numerical methods such as the Newton-Raphson method or software tools like calculators or computer algebra systems to approximate the solutions.

If you're looking for exact solutions, you may want to explore advanced techniques like Cardano's formula for cubic equations, but be aware that these methods can be complex and involve multiple steps.

Without using numerical methods or advanced techniques, it's not possible to find exact solutions for this cubic equation.