Question

Помогите/Даю 30 баллов
Решите систему уравнений графическим способом система


x^2+y^2=16
y=-x^2

Answer 1

$\left\{\begin{array}{l}x^2+y^2=16\\y=-x^2\end{array}\right\ \ \left\{\begin{array}{l}x^2+y^2=16\\x^2=-y\end{array}\right\ \ \left\{\begin{array}{l}y^2-y-16=0\\x^2=-y\end{array}\right\ \ \left\{\begin{array}{l}y_{1,2}=\dfrac{1\pm \sqrt{65}}{2}\\x^2=-y\end{array}\right$

$x^2_1=\dfrac{-1+\sqrt{65}}{2}>0\ \ ,\ \ x_2^2=\dfrac{-1-\sqrt{65}}{2}<0\ \ ne\ \ podxodit\\\\\\x_1=\sqrt{\dfrac{\sqrt{65}-1}{2}}\ \ ,\ \ x_2=-\sqrt{\dfrac{\sqrt{65}-1}{2}}\\\\\\Otvet:\ \ \Big(\ \sqrt{\dfrac{\sqrt{65}-1}{2}}\ ;\ \dfrac{1-\sqrt{65}}{2}\ \Big)\ ,\ \ \Big(-\sqrt{\dfrac{\sqrt{65}-1}{2}}\ ;\ \dfrac{1-\sqrt{65}}{2}\ \Big)\ .$