100 баллов!! 3tg²x - 2tgx - 1 = 0

Ответ:

To solve the given equation 3tg²x - 2tgx - 1 = 0 for the variable tgx, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by:

\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \]

In this case, we have a = 3, b = -2, and c = -1. Substituting these values into the quadratic formula, we get:

\[ tgx = \frac{{2 \pm \sqrt{{(-2)^2 - 4(3)(-1)}}}}{{2(3)}} \]

\[ tgx = \frac{{2 \pm \sqrt{{4 + 12}}}}{{6}} \]

\[ tgx = \frac{{2 \pm \sqrt{{16}}}}{{6}} \]

\[ tgx = \frac{{2 \pm 4}}{{6}} \]

So the solutions for tgx are:

\[ tgx = \frac{{2 + 4}}{{6}} \]

\[ tgx = \frac{6}{6} \]

\[ tgx = 1 \]

and

\[ tgx = \frac{{2 - 4}}{{6}} \]

\[ tgx = \frac{{-2}}{6} \]

\[ tgx = -\frac{1}{3} \]

Therefore, the solutions for tgx are tgx = 1 and tgx = -1/3.

Пошаговое объяснение:

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