Question

Решить уравнение: 3ctg^2x=2tg^2x-5

Answer 1

$\frac{3}{ tgx^{2} }=2 tgx^{2}-5 \\ \frac{3}{t}=2t-5 | *t \\ 3=2 t^{2} -5 t \\ 2 t^{2}-5t-3=0$
$D= \sqrt{25+4*3*2}= \sqrt{49}=7 \\ x_{1}= \frac{5+7}{4}=3 \\ x_{2}= \frac{5-7}{4}=-0.5$
$tgx^{2} =3 \\ 1)tgx= \sqrt{3} \\ tgx= \frac{ \pi }{3}+ \pi n \\ 2)tgx=- \sqrt{3} \\ tgx= \frac{2 \pi }{3}+ \pi n,$