Question

Решить систему уравнений

Answer 1

$left { {{x^2-xy-20y^2=0} atop {x^2+2xy-3y^2=32}} right.; left { {{x^2-5xy+4xy-20y^2=0} atop {x^2+2xy+y^2-4y^2=32}} right. ; left { {{x(x-5y)+4y(x-5y)=0} atop {(x+y)^2-(2y)^2=32}} right.; \ left { {{(x+4y)(x-5y)=0} atop {(x+y-2y)(x+y+2y)=32}} right.; left { {{x=-4y or x=5y} atop {(x-y)(x+3y)=32}} right. ;\ left { {{x=-4y} atop {(-4y-y)(-4y+3y)=32}} right. or left { {{x=5y} atop {(5y-y)(5y+3y)=32}} right.;$

$left { {{x=-4y} atop {5y^2=32}} right. or left { {{x=5y} atop {32y^2=32}} right.;\ left { {{x=-4y} atop {y=pm 4sqrt{frac{2}{5}} }} right. or left { {{x=5y} atop {y=pm1}} right.;\ left { {{x=mp16 sqrt{ frac{2}{5} } } atop {y=pm 4sqrt{frac{2}{5}} }} right. or left { {{x=pm5} atop {y=pm1}} right..$

Answer: $(-16 sqrt{ frac{2}{5}}; 4 sqrt{ frac{2}{5}}), (+16 sqrt{ frac{2}{5}}; -4 sqrt{ frac{2}{5}}), (5; 1), (-5; -1)$