X^2-y^2=16 xy=15 Решите систему уравнений

x=15/y 225/y²-y²=16 225-y^4-16y²=0 y≠0 y²=a a²+16a-225=0 D=256+900=1156 √D=34 a1=(-16-34)/2=-25⇒y²=-25 нет решения a2=(-16+34)/2=9⇒y²=9⇒y=+-3 x1=15/(-3)=-5 x2=15/3=5 (-5;-3);(5;3)

[latex]\left \{ {{ x^{2} - y^{2} =16} \atop {xy=15} } \right. \\ \left \{ {{ x^{2} - y^{2} =16} \atop {y= \frac{15}{x} } } \right. \\ x^{2} - (\frac{15}{x})^{2} =16 \\ x^{2} - \frac{225}{ x^{2} } =16 \\ [/latex] Замена: [latex]x^{2} = t \\ t - \frac{225}{t} = 16 \\ t^{2} - 16t - 225 = 0 \\ t=25, t = - 9 \\ \\ x^{2} =25 =\ \textgreater \ x=5, x=-5 \\ \\ [/latex] [latex]y= \frac{15}{5} = 3, y= \frac{15}{-5} = -3 \\ [/latex] ОТвет: ( 5;3 ),  ( -5;-3 ).