Найти решения системы: х²-у²=3 ху=-2

x²-y²=3 x=2 y=-1 4-1=3 2*-1=-2

[latex] \left \{ {{x^2-y^2=3} \atop {xy=-2}} \right. [/latex]   ⇔   [latex]\left \{ {{x^2-(- \frac{2}{x})^2=3} \atop {y=- \frac{2}{x} }} \right.[/latex] [latex]x^2-(- \frac{2}{x})^2=3\\x^2-\frac{4}{x^2}=3\\x^4-3x^2-4=0[/latex] x²=a  ⇒  x⁴=a²     a²-3a-4=0       D = 9-4(-4)=25=5² a₁=4    u    a₂=-1 x²=4          x²=-1⇒ ∅ x₁=-2  x₂=2 [latex] \left \{ {{x_1=-2} \atop {y=1}} \right. [/latex]    [latex] \left \{ {{x_2=2} \atop {y_2=-1}} \right. [/latex]