Question

Чи е пара чисел (1; -2) розв'язком системи рівнянь
у²-x²=3,
2x+y=4?

Answer 1

Ответ: (1;2)  (13/3;-14/3).

Объяснение:

$\displaystyle\\\left \{ {{y^2-x^2=3} \atop {2x+y=4}} \right. \ \ \ \ \ \left \{ {{y^2-x^2=3} \atop {y=4-2x}} \right. \ \ \ \ \left \{ {{(4-2x)^2-x^2=3} \atop {y=4-2x}} \right. \\\\\\\left \{ {{16-16x+4x^2-x^2=3} \atop {y=4-2x}} \right.\ \ \ \ \left \{ {{3x^2-16x+13=0} \atop {y=4-2x}} \right. \ \ \ \ \left \{ {{3x^2-3x-13x+13=0} \atop {y=4-2x}} \right. \\\\\\\left \{ {{3x*(x-1)-13*(x-1)=0} \atop {y=4-2x}} \right.\ \ \ \ \left \{ {{(x-1)*(3x-13)=0} \atop {y=4-2x}} \right.$

$\displaystyle\\\left \{ {{x_1=1\ \ \ \ x_2=\frac{13}{3} } \atop {y_1=2\ \ \ \ y_2=-\frac{14}{3} }} \right. .$