Question

2x^2+4xy-5y=1
x^2+xy-6y^2=0
Эти два уравнения в системе

Answer 1

$left { {{2x^2+4xy-5y^2=1} atop {x^2+xy-6y^2=0}} right. \\x^2+xy-6y^2=0; |:y^2ne 0\\(frac{x}{y})^2+frac{x}{y}-6=0\\t=frac{x}{y}; ,; ; t^2+t-6=0; ; ,; ; t_1=2; ,; t_2=-3; ; (teorema; Vieta)\\a); ; frac{x}{y}=2; ; to ; ; x=2y\\2x^2+4xy-5y^2=2(2y)^2+4cdot 2ycdot y-5y^2=8y^2+8y-5y^2=11y^2=1\\y=pm frac{1}{sqrt{11}}; ; to ; ; ; ; x=pm frac{2}{sqrt{11}}\\b); ; frac{x}{y}=-3; ; to ; ; x=-3y\\2x^2+4xy-5y^2=18y^2-12y^2-5y^2=y^2=1\\y=pm 1; ; to ; ; x=mp3$

$Otvet:; ; (frac{2}{sqrt{11}},frac{1}{sqrt{11}} ); ,; (-frac{2}{sqrt{11}},-frac{1}{sqrt{11}}); ,; (1,-3); ,; (-1,3); .$