Question

система уравнений.

двойная замена переменных

 

{ xy(x-1)(y-1)=72

{ (x+1)(y+1)=20

Answer 1

xy(xy+1-(x+y))=72

1+(x+y)+xy=20

 

x+y=t

xy=s

 

s(s+1-t)=72    s(s+1-19+s)=72   2s(s-9)=72   s^2-9s-36=0  s1=12  s2=-3

s+t=19 t=19-s                                                                 t1=7      t2=22

  

x+y=7

xy=12   x=3 y=4

             x=4 y=3

 

x+y=22

xy=-3           x3=11+2sqrt(31)      y3=11-2sqrt(31)

                    x4=11-2sqrt(31)       y4=11+2sqrt(31)