Решить систему:
[tex] \left \{ {{ \frac{x+y}{x-y}+6 \frac{x-y}{x+y} =5 } \atop { 5y^{2} - x^{2} =1 }} \right. [/tex]
[tex] \left \{ {{ \frac{x+y}{x-y}+6 \frac{x-y}{x+y} =5 } \atop { 5y^{2} - x^{2} =1 }} \right. [/tex]
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Answers & Comments
(x+y)/(x-y)=t
t+6/t=5
t^2-5t+6=0
t1=2 t2=3
1) (x+y)/(x-y)=2
x+y=2x-2y
x=3y
5y^2-9y^2=1
-4y^2=1 нет решений.
2)(x+y)/(x-y)=3
x+y=3x-3y
2x=4y
x=2y
5y^2-4y^2=1
y^2=1
y=+-1
x=+-2
Ответ: (2,1);(-2;-1)