Question

решите систему уравнений

х/у=1/4
у^2 - х^2 = 60​

Answer 1

$\left \{ {{\frac{x}{y}=\frac{1}{4}} \atop {y^{2}-x^{2}=60}} \right.\\\\\left \{ {{y=4x} \atop {(4x)^{2}-x^{2}=60}} \right. \\\\\left \{ {{y=4x} \atop {16x^{2}-x^{2}=60}} \right.\\\\\left \{ {{y=4x} \atop {15x^{2}=60}} \right.\\\\\left \{ {{y=4x} \atop {x^{2}=4}} \right.\\\\1)x_{1}=-2\\\\y_{1}=4*(-2)=-8\\\\2)x_{2}=2\\\\y_{2}=4*2=8\\\\Otvet:\boxed{(-2;-8),(2;8)}$