Question

Rezolvati sistemul:
X^2-Y^2=1
2XY=3

Answer 1

2xy=3=> y=3/2 x  Inlocuieasti   in   prima   ecuatie
x²-(3/2x)²=1

x²-9/4*x²=1
Faci   substitutia   x²=t   t≥0
t-9/4t=1
4t²-9=4t
4t²-4t-9=0
Determinantul Δ=16+144=160
x1=(4-√160)/4=1-√10<0 nu   se    accepta
x2=(4+√160)/4=1+√10>0  se   accepta
x²=1+√10
x1=-(1+√10)
x2=1+√10