Question

Решите систему уравнений $left { {{x - y=7} atop {x^2+y^2=9-2xy}} right.$

Answer 1

$x-y=7;\\y=x-7;\\x^2+y^2=9-2xy;\\x^2+(x-7)^2=9-2x(x-7);\\x^2+x^2-14x+49=9-2x^2+14x;\\4x^2-28x+40=0;\\x^2-7x+8=0;\\D=(-7)^2-4*1*8=49-32=17;\\x_1=frac{7+sqrt{17}}{2};\\x_2=frac{7-sqrt{17}}{2};\\y_1=frac{7+sqrt{17}}{2}-7=frac{-7+sqrt{17}}{2};\\y_2=frac{7-sqrt{17}}{2}-7=frac{-7-sqrt{17}}{2};\\(frac{7+sqrt{17}}{2};frac{-7+sqrt{17}}{2}); (frac{7-sqrt{17}}{2};frac{-7-sqrt{17}}{2})$