Question

{x^2-2xy+y^2=4
{xy=3

Answer 1

х=3/у
(3/у)²-2(3/у)у+у²=4

х=3/у
9/у²-6+у²=4

х=3/у
9-6у²+у^4=4у²
введем замену у²=t

х=3/√t
9-6t+t²-4t=0

х=3/√t
t²-10t+9=0

Д=100-36=64=8²
t1=(10+8)/2=9
t2=(10-8)/2=1

х=3/у
y²=t

y²=9. y²=1
х=3/у. х=3/у

y1=3. y1=1
y2=-3. y2=-1
x1=1. x1=3
x2=-1. x2=-3