Question

Решите систему уравнений
{2x+y=5
{3x^2-y^2=11

Answer 1

у=5-2х, подстановка

3х²-у²=11

3х²-(5-2х)²=11

3х²-(25-20х+4х²)=11

3х²-25+20х-4х²-11=0

-х²+20х-36=0

х²-20х+36=0

D1=(b/2)²-ac

D1=100-36=64=8²

x1,2=(-b/2+-√D1)/a

x1=10+8=18

x2=10-8=2

у1=5-2х1=5-36=-31

у2=5-2х2=5-4=1

ответ: (18;-31) и (2; 1).

Answer 2

$\left \{ {{2x+y=5} \atop {3x^2-y^2=11}} \right.\; \left \{ {{y=5-2x\qquad \quad \qquad } \atop {3x^2-(25-20x+4x^2)=11}} \right.\; \left \{ {{y=5-2x} \atop {-x^2+20x-36=0}} \right.\\\\x^2-20x+36=0\; \; ,\; \; D/4=64\\\\x_1=2\; ,\; \; x_2=18\\\\y_1=5-2\cdot 2=1\; \; ,\; \; y_2=5-2\cdot 18=-31\\\\Otvet:\; \; (2,1)\; ,\; \; (18,-31)\; .$