Question

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

Answer 1

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