Question

Решите систему уравнений:

$\left \{ {{4x - y=3} \atop {2x^{2 + y^{2} } =3}} \right.$

Answer 1

$\left \{ {{4x-y=3} \atop {2x^2+y^2=3}} \right. \; \left \{ {{y=4x-3} \atop {2x^2+(4x-3)^2=3}} \right. \\\\2x^2+16x^2-24x+9=3\\\\18x^2-24x+6=0\\\\3x^2-4x+1=0\\\\x_1=1,\; \; x_2=\frac{1}{3}\\\\y_1=4-3=1,\; \; y_2=4\cdot \frac{1}{3}-3=-\frac{5}{3}\\\\Otvet:\; (1,1),\; (\frac{1}{3},-\frac{5}{3}).$