Question

Найти решения системы: х²-у²=3 ху=-2

Answer 1

X²-y²=3

x=2
y=-1
4-1=3
2*-1=-2

Answer 2

$\left \{ {{x^2-y^2=3} \atop {xy=-2}} \right.$   ⇔   $\left \{ {{x^2-(- \frac{2}{x})^2=3} \atop {y=- \frac{2}{x} }} \right.$

$x^2-(- \frac{2}{x})^2=3\\x^2-\frac{4}{x^2}=3\\x^4-3x^2-4=0$

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

$\left \{ {{x_1=-2} \atop {y=1}} \right.$    $\left \{ {{x_2=2} \atop {y_2=-1}} \right.$