Question

Умоляю, помогите! Решите систему 1/y-1 - 1/y+1 =1/x , y^2 - x - 5=0

Answer 1

$\left \{ {{\frac{1}{y-1}}-\frac{1}{y+1}=\frac{1}{x}} \atop {y^{2}-x-5=0 }} \right. \\\\\left \{ {{\frac{y+1-y+1}{y^{2}-1 } =\frac{1}{x} } \atop {y^{2}-x-5=0}} \right.\\\\\left \{ {{\frac{2}{y^{2}-1 }=\frac{1}{x}} \atop {y^{2} -x-5=0 }} \right. \\\\\left \{ {{y^{2} -1=2x} \atop {x=2}} \right. \\\\-\left \{ {{y^{2}-2x=1 } \atop {y^{2}-x=5 }} \right.\\------\\ -x=-4\\\\x=4\\\\y^{2} =x+5=4+5=9\\\\y_{1}=-3\\\\y_{2}=3\\\\Otvet:\boxed{(4;-3),(4;3)}$