Question

Решите систему уравнений. пожалуйста! очень нужно

Answer 1

$\begin{cases}x^2+2y^2=17\\-\\x^2+2yx=-3\end{cases}\\2y^2-2yx=20\\y^2-yx=10\\x=\frac{y^2-10}{y}\\\\\frac{(y^2-10)^2}{y^2}+2y^2=17\\(y^2-10)^2=17y^2-2y^4\\y^4-20y^2+100=17y^2-2y^4\\3y^4-37y^2+100=0;y^2=a;a>0\\3a^2-37a+100=0\\a_{1,2}=\frac{37^+_-13}{6}\\a_1=4\ ;a_2=\frac{25}{3}\\y^2=4\ ;y^2=\frac{25}{3}$
$\\y_{1,2}=^+_-2\ y_{3,4}=^+_-\frac{5}{\sqrt3}\\x_1=\frac{4-10}{2}=-3\\x_2=\frac{4-10}{-2}=3\\x_3=\frac{(\frac{25}{3}-10)\sqrt3}{5}=\frac{-\frac{5}{3}*\sqrt3}{5}=-\frac{1}{\sqrt3}\\x_4=\frac{(\frac{25}{3}-10)\sqrt3}{-5}=\frac{1}{\sqrt3}\\\\OTBET:(-3;2);(3;-2);(-\frac{1}{\sqrt3};\frac{5}{\sqrt3});(\frac{1}{\sqrt3};-\frac{5}{\sqrt3})$