Question

ДАЮ 50 Б СРОЧНО !!!
Решите систему уравнений |3x^(2)+2xy+y^(2)=2
|x^(2)+2xy+5y^(2)=4

Answer 1

$left { {{3x^2+2xy+y^2=2, |cdot (-2)} atop {x^2+2xy+5y^2=4}} right.; oplus ; left { {{3x^2+2xy+y^2=2} atop {-5x^2-2xy+3y^2=0}} right. \\-5x^2-2xy+3y^2=0, Big |:x^2ne 0\\-5-2cdot frac{y}{x}+3cdot (frac{y}{x})^2=0; ; ,; ; t=frac{y}{x}; ; to ; ; 3t^2-2t-5=0; ,\\D/4=1+15=16; ,; ; t_1=-1; ,; t_2=frac{5}{3}\\a); ; frac{y}{x}=-1; ,; ; y=-x; ,\\3x^2-2x^2+x^2=2; ,; 2x^2=2; ,; x^2=1; ,; x=pm 1; ; ,; ; y=mp 1\\b); ; frac{y}{x}=frac{5}{3}; ,; ; y=frac{5x}{3}; ,\\3x^2+frac{10x^2}{3}+frac{25x^2}{9}=2; ,; ; frac{82x^2}{9}=2; ,; x^2=frac{9}{41}\\x=pm frac{3}{sqrt{41}}; ; ,; ; y=pm frac{5}{sqrt{41}}$

$Otvet:; ;(1,-1); ,; (-1,1); ,; ; (frac{3}{sqrt{41}}, ,, frac{5}{sqrt{41}}); ,; ; (-frac{3}{sqrt{41}}, ,, -frac{5}{sqrt{41}}); .$