Question

Система неравенств x^2-y^2=16 xy=15

Answer 1

X²-y²=16, xy=15
y=15/x
x²-225/x²=16
xˇ4-225=16x²
xˇ4-16x²-225=0
x²=z
z²-16z-225=0,D=256+900=1156,√1156=34
z1=(16+34)/2=50/2=25
z2=(16-34)/2=-18/2=-9 net rešeniem
x²=25
/x/=5, x1=5,x2=-5
y1=3,y2=-3
Otvet: /5,3/, /-5,-3/