Question

Найдите такие x и y такие что (x^2+xy+y^2)=1993 и (х-у)=1

Answer 1

$\left \{ {{x^2+xy+y^2=1993} \atop {x-y=1}} \right. \\ \left \{ {{(x^2-2xy+y^2)+3xy=1993} \atop {x-y=1}} \right. \\ \left \{ {{(x-y)^2+3xy=1993} \atop {x-y=1}} \right. \\ \left \{ {{1+3xy=1993} \atop {x-y=1}} \right.$
$\left \{ {{1+3y(y+1)=1993} \atop {x=y+1}} \right. \\ 3y^2+3y+1=1993 \\ 3y^2+3y-1992=0 \\ D = 9+12*1992=23925 \\ y_{1,2} = \frac{-3+-5 \sqrt{957} }{6} \\ x_{1,2}= \frac{-3+-5 \sqrt{957} }{6} +1$