Question

решите систему уравнений
2y-x=7
x^2-xy-y^2=20

Answer 1

$displaystyleleft { {{2y-x=7~~~~~~~~~~} atop {x^2-xy-y^2=20}} right.\\left { {{x=2y-7~~~~~~~~~~~~~~~~~~~~~~~~~~} atop {(2y-7)^2-(2y-7)y-y^2=20}} right.\\left { {{x=2y-7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~} atop {4y^2-28y+49-2y^2+7y-y^2=20}} right.\\left { {{x=2y-7~~~~~~~~~~} atop {y^2-21y+29=0}} right.$

$y^2-21y+29=0\D=21^2-4cdot 29=441-116=325=big(5sqrt {13}big)^2\\y_1=dfrac{21-5sqrt{13}}2=10,5-2,5sqrt{13}\\~~~~~~~~~x_1=2cdot big(10,5-2,5sqrt{13}big)-7=14-5sqrt{13}\\y_2=dfrac{21+5sqrt{13}}2=10,5+2,5sqrt{13}\\~~~~~~~~~x_2=2cdot big(10,5+2,5sqrt{13}big)-7=14+5sqrt{13}$

Ответ : (14-5√13; 10,5-2,5√13) ; (14+5√13; 10,5+2,5√13)