2х2-у2=46,  ху=10 решите систему уравнений

[latex]\left \{ {{2x^2-y^2=46} \atop {xy=10}} \right.\\ \left \{ {{2x^2-(\frac{10}{x})^2=46} \atop {y=\frac{10}{x}}} \right.\\ \left \{ {{2x^4-46x^2-100=0} \atop {y=\frac{10}{x}}} \right.\\ D=46^2+2*4*100=2116+800=2916=54^2\\ x_{1}=\frac{46-54}{2*2}=\frac{-8}{4}=-2\\ x_{2}=\frac{46+54}{2*2}=\frac{100}{4}=25\\ y_{1}=-5\\ y_{2}=0,4\\[/latex] Ответ:{(-2;-5);(25;0,4)}