Question

{x²-y=-1
{2x+y=9
хеееелп​

Answer 1

Ответ:

$\left \{ {{x^{2} -y=-1} \atop {2x+y=9}} \right.\\\left \{ {{y=x^{2} +1} \atop {y=9-2x}} \right.\\\left \{ {{y=x^{2} +1} \atop {x^{2} +1=9-2x}} \right.\\\\x^{2} +1=9-2x\\x^{2} +2x+1-9=0 \\x^{2} +2x-8=0\\D=2^{2} -4*1*(-8)=4+32=36\\x_{1}=\frac{-2+\sqrt{36} }{2*1}=\frac{-2+6}{2}=\frac{4}{2}=2\\x_{2}=\frac{-2-\sqrt{36} }{2*1}=\frac{-2-6}{2}=\frac{-8}{2}=-4\\\\\left \{ {{y=x^{2} +1} \atop {x=2}} \right.\\\left \{ {{y=2^{2}+1 } \atop {x=2}} \right. \\\left \{ {{y=5} \atop {x=2}} \right.$            

$\left \{ {{y=x^{2} +1} \atop {x=-4}} \right.\\\left \{ {{y=-4^{2}+1 } \atop {x=-4}} \right.\\\left \{ {{y=17} \atop {x=-4}} \right. \\\\\left \{ {{x_{1} =2} \atop {y_{1} =5}} \right.\\\left \{ {{x_{2} =-4} \atop {y_{2} =17}} \right.$

Проверка:

$\left \{ {{x^{2} -y=-1} \atop {2x+y=9}} \right. \\\left \{ {{2^{2} -5=-1} \atop {2*2+5=9}} \right. \\\left \{ {{4-5=-1} \atop {4+5=9}} \right. \\\left \{ {{-1=-1} \atop {9=9}} \right. \\\\\\\left \{ {{x^{2} -y=-1} \atop {2x+y=9}} \right.\\\left \{ {{-4^{2}-17 =-1} \atop {2*(-4)+17=9}} \right.\\\left \{ {{16-17=-1} \atop {-8+17=9}} \right. \\\left \{ {{-1=-1} \atop {9=9}} \right.$