2ctg в квадрате x + ctgx -1=0

2ctg²x + ctgx - 1 = 0 ctgx = t 2t² + t - 1 = 0 D = 1² - 4· 2·(-1) = 1 + 8 = 9 [latex] \sqrt{D } =3[/latex] [latex]t _{1} = \frac{-1+3}{4}= \frac{2}{4}= \frac{1}{2} [/latex] [latex]t _{2} = \frac{-1-3}{4} = \frac{-4}{4} =-1[/latex] [latex] \left \{ {{ctgx= \frac{1}{2} } \atop {ctgx=-1}} \right. [/latex] [latex]x=arcctg \frac{1}{2} + \pi k,[/latex] k∈Z [latex]x = \frac{3 \pi }{4} + \pi k,[/latex] k∈Z