Question

Розвяжіть систему рівнянь:
X - 2y = 1
X² - 2y² = 7​

Answer 1

Пояснення:

$\displaystyle\\\left \{ {{x-2y=1} \atop {x^2-2y^2=7}} \right. \ \ \ \ \ \ \left \{ {{x=2y+1} \atop {(2y+1)^2-2y=7}} \right. \ \ \ \ \ \ \left \{ {{x=2y+1} \atop {4y^2+4y+1-2y^2=7}} \right.\\\\\\\left \{ {{x=2y+1} \atop {2y^2+4y-6=0\ |:2}} \right. \ \ \ \ \ \ \ \left \{ {{x=2y+1} \atop {y^2+2y-3=0}} \right. \ \ \ \ \ \ \left \{ {{x=2y+1} \atop {y^2+3y-x-3=0}} \right.$

$\displaystyle\\\left \{ {{x=2y+1} \atop {y*(y+3)-(x+3)=0}} \right. \ \ \ \ \left \{ {{x=2y+1} \atop {(y+3)*(x-1)=0}} \right. \ \ \ \ \left \{ {{x_1=-5 \ \ \ x_2=3} \atop {y_1=-3\ \ \ \ y_2=1} \right..$

Відповідь: (-5;-3),  (3;1).