Question

Розв'яжіть систему рівнянь х²+2y=5, y-x=1

Answer 1

$\displaystyle\bf\\\left \{ {x^{2} +2{y=5} \atop {y-x=1}} \right. \\\\\\\left \{ {{y=x+1} \atop {x^{2} +2\cdot(x+1)=5}} \right. \\\\\\\left \{ {{y=x+1} \atop {x^{2} +2x+2-5=0}} \right.\\\\\\\left \{ {{y=x+1} \atop {x^{2} +2x-3=0}} \right.\\\\\\x^{2} +2x-3=0\\\\Teorema \ Vieta \ :\\\\x_{1} + x_{2} =-2\\\\x_{1} \cdot x_{2} =-3\\\\x_{1} =-3 \ \ \ ; \ \ \ x_{2} =1\\\\y_{1}=-3+1=-2\\\\y_{2}=1+1=2\\\\\\Otvet \ : \ (-3 \ ; \ -2) \ \ , \ \ (1 \ ; \ 2)$