Question

Решите систему уравнений 100 Баллов

Answer 1

Ответ:

Объяснение:

$\displaystyle\\\left \{ {{x^2-3xy+y^2=11~~~~~~~|\cdot36} \atop {2x^2-5xy+2y^2=36~~~~|\cdot11}} \right.\\\\\\\left \{ {{36x^2-108xy+36y^2=396} \atop {22x^2-55xy+22y^2=396}} \right.$

вычтем

$14x^2-53xy+14y^2=0\\\\14x^2-49xy-4xy+14y^2=0\\\\7x(2x-7y)-2y(2x-7y)=0\\\\(2x-7y)(7x-2y)=0\\\\1)x=\dfrac{7y}{2} \\\\\bigg(\dfrac{7y}{2} \bigg)^2-3y\cdot\dfrac{7y}{2} +y^2=11\\\\\dfrac{49y^2}{4} -\dfrac{21y^2}{2} +y^2=11~~~~~~~~~~~|\cdot4\\\\49y^2-42y^2+4y^2=44\\11y^2=44\\y^2=4\\y=\pm2;~~x=\pm7\\\\2)y=\dfrac{7x}{2} \\\\49x^2-42x^2+4x^2=44\\x^2=4\\x=\pm2;~~~y=\pm7\\\\Otvtt:(-7;-2)~(-2;-7)~(2;7)~(7;2)$