Question

Решите систему уравнений
X²-2y=54
Y=x-3

Answer 1

Ответ:

(x; y) ∈ {(8; 5), (-6; -9)}

Объяснение:

$\displaystyle \tt \left \{ {{x^2-2 \cdot y=54} \atop {y=x-3}} \right.\\\\\left \{ {{x^2-2 \cdot (x-3)-54=0} \atop {y=x-3}} \right. \\\\\left \{ {{x^2-2 \cdot x+6-54=0} \atop {y=x-3}} \right. \\\\\left \{ {{x^2-2 \cdot x-48=0} \atop {y=x-3}} \right.$

$\displaystyle \tt \left \{ {{x^2-8 \cdot x+6 \cdot x-48=0} \atop {y=x-3}} \right. \\\\\left \{ {{(x-8) \cdot x+6 \cdot (x-8)=0} \atop {y=x-3}} \right. \\\\\left \{ {{(x-8) \cdot (x+6)=0} \atop {y=x-3}} \right. \\\\\left \{ {{x-8=0, \; x+6 =0} \atop {y=x-3}} \right.\\\\ \left \{ {{x_1=8 \;, \; x_2=-6} \atop {y_1=8-3=5, y_2=-6-3=-9}} \right.\\\\(x; y) \in \{ (8; 5), (-6; -9) \}$