Question

Найти $x+y$ , если $tgx$ , $tgy$ - корни уравнения $x^{2}-(1+ sqrt{3} )x+ sqrt{3} =0$

Answer 1

$x^2-(1+sqrt3)x+sqrt3=0\D=1+2sqrt3+3-4sqrt3=(1-sqrt3)^2\x_1=1\x_2=sqrt3$

$tg x=1\x={piover4}+pi k, kin Z\tg y=sqrt3\y={piover3}+pi l,lin Z$

$x+y={7piover 12}+pi m, min Z$