Question

розвяжіть систему рівнянь x^2+2y^2=5 y-x=1

Answer 1

Объяснение:

$\left \{ {{x^2+2y^2=5} \atop {y-x=1}} \right. \ \ \ \ \ \ \left \{ {{(y-1)^2+2y^2=5} \atop {x=y-1}} \right. \ \ \ \ \left \{ {{y^2-2y+1+2y^2=5} \atop {x=y-1}} \right.\ \ \ \ \ \left \{ {{3y^2-2y-4=0} \atop {x=y-1}} \right.$

$\left \{ {{D=52\ \ \ \ \sqrt{D} =2\sqrt{13} } \atop {x=y-1}} \right. \ \ \ \ \ \left \{ {{y_1=\frac{1}{3} -\frac{\sqrt{13} }{3} \ \ \ \ y_2=\frac{1}{3}+\frac{\sqrt{13} }{3} } \atop {x_1=-\frac{2}{3} -\frac{\sqrt{13} }{3}\ \ \ \ x_2=-\frac{2}{3}+\frac{\sqrt{13} }{3} }} \right. .$