Question

Решить систему уравнений       (   3x - y = 5        3x2 + y2 = 13                     

Answer 1

$begin{cases}3x-y=5\3x^2+y^2=13end{cases}Rightarrowbegin{cases}y=3x-5\3x^2+(3x-5)^2=13end{cases}\3x^2+(3x-5)^2=13\ 3x^2+9x^2-30x+25=13\12x^2-30x+12=0;;;div6\2x^2-5x+2=0\D=25-4cdot2cdot2=9\x_1=frac12;;x_2=2\begin{cases}y=3cdotfrac12-5\x=frac12end{cases}quadquadquadbegin{cases}y=3cdot2-5\x=frac12end{cases}\begin{cases}y=-3frac12\x=2end{cases}quadquadquadbegin{cases}y=1\x=2end{cases}$