Question

решить систему рационального уравнения х в 2 + у в 2 = 41 и у- х = 1

Answer 1

$\left \{ {{ x^{2} +y^{2}=41} \atop {y-x=1}} \right \\ \left \{ {{x^2+y^2=41} \atop {x=-1+y}} \right. \\ (-1+y)^2+y^2=41 \\ y=5 \\ y=-4 \\ x=-1+5 \\ x=-1-4 \\ x=4 \\ x=-5$$( x_{1},y_1)=4,5 \\ (x_2,y_2)=(-5,-4) \\ \left \{ {{4^2+5^2=41} \atop {5-4=1}} \right. \\ \left \{ {{(-5)^2+(-4)^2=41} \atop {-4-(-5)=1}} \right. \\ \left \{ {{41=41} \atop {1=1}} \right. \\ (x_1,y_1)=(4,5) \\ (x_2,y_2)=(-5,-4)$