Question

$left { {{3x^{2}+5xy-4y^{2}=-2} atop {5x^{2}+9xy-2y^{2}=0}} right.$
Решите систему уравнений

Answer 1

$left { {{3x^{2}+5xy-4y^{2}=-2} atop {5x^{2}+9xy-2y^{2}=0}} right. \ left { {{3x^{2}+5xy-4y^{2}=-2} atop {5x^{2}+10xy-xy-2y^{2}=0}} right. \ left { {{3x^{2}+5xy-4y^{2}=-2} atop {5x(x+2y)-y(x+2y)=0}} right. \ left { {{3x^{2}+5xy-4y^{2}=-2} atop {(x+2y)(5x-y)=0}} right.$

$left { {{3x^{2}+5xy-4y^{2}=-2} atop {x+2y=0}} right. \ x=-2y \ 3(-2y)^2+5(-2y)y-4y^2=-2 \ 12y^2-10y^2-4y^2=-2 \ y^2=1 \ y_1=1 \ y_2=-1 \ x_1=-2 \ x_2=2$

$left { {{3x^{2}+5xy-4y^{2}=-2} atop {5x-y=0}} right. \ y=5x \ 3x^2+5x(5x)-4(5x)^2=-2 \ 3x^2+25x^2-100x^2=-2 \ x^2= frac{1}{36} \ x_3= frac{1}{6} \ x_4=-frac{1}{6} \ y_3=frac{5}{6} \ y_4=-frac{5}{6}$

Ответ: (-2; 1); (2; -1); (1/6; 5/6); (-1/6; -5/6)