Question

Решите систему уравнений !
(у+х)/(у-х) - 5(у-х)/(у+х)=6
х^2-у^2=13

Answer 1

$\left \{ {{ \frac{y+x}{y-x}+ \frac{5(y-x)}{y+x} =6 } \atop {x^2+y^2=13}} \right. \\ \\ a= \frac{y+x}{y-x} \\ \\ a+ \frac{5}{a} =6 \\ \\ a^2-6a+5=0 \\ \\ D=16 \\ a_{1} =5; a_{2} =1 \\ \\ 1) \left \{ {{ \frac{y+x}{y-x} =5} \atop {x^2+y^2=13}} \right. \\ \\ \left \{ {{ y+x=5y-5x} \atop {x^2+y^2=13}} \right. \\ \\ \left \{ {{y=1.5x} \atop {x^2=4}} \right.[tex] \left \{ {{y=3} \atop {x=2}} \right. ; \left \{ {{y=-3} \atop {x=-2}} \right. \\ \\ 2) \left \{ {{ \frac{y+x}{y-x} =1} \atop {x^2+y^2=13}} \right. \\ \\ \left \{ {{ y+x=y-x} \atop {x^2+y^2=13}} \right. \\ \\ \left \{ {{x=0} \atop {y^2=13}} \right. \\ \\ \left \{ {{x=0} \atop {y= \sqrt{13} }} \right. ; \left \{ {{x=0} \atop {y= -\sqrt{13} }} \right.$