x^2+y^2=49 (x+y)^2=27

$$x^{2} + y^{2} = 49$$

2
(x + y) = 27

$$left(x + yright)^{2} = 27$$

$$x_{1} = – frac{1}{11} left(-7 – sqrt{- frac{3 sqrt{213}}{2} + frac{49}{2}}right) sqrt{- frac{3 sqrt{213}}{2} + frac{49}{2}} left(- sqrt{- frac{3 sqrt{213}}{2} + frac{49}{2}} + 7right)$$
=
$$frac{1}{44} sqrt{- 3 sqrt{213} + 49} left(3 sqrt{426} + 49 sqrt{2}right)$$
=

6.81115109794150

$$y_{1} = – sqrt{- frac{3 sqrt{213}}{2} + frac{49}{2}}$$
=
$$- frac{1}{2} sqrt{- 6 sqrt{213} + 98}$$
=

-1.61499867523486

$$x_{2} = frac{1}{11} left(-7 + sqrt{- frac{3 sqrt{213}}{2} + frac{49}{2}}right) sqrt{- frac{3 sqrt{213}}{2} + frac{49}{2}} left(sqrt{- frac{3 sqrt{213}}{2} + frac{49}{2}} + 7right)$$
=
$$- frac{1}{44} sqrt{- 3 sqrt{213} + 49} left(3 sqrt{426} + 49 sqrt{2}right)$$
=

-6.81115109794150

$$y_{2} = sqrt{- frac{3 sqrt{213}}{2} + frac{49}{2}}$$
=
$$frac{1}{2} sqrt{- 6 sqrt{213} + 98}$$
=

1.61499867523486

$$x_{3} = – frac{1}{11} left(-7 – sqrt{frac{3 sqrt{213}}{2} + frac{49}{2}}right) sqrt{frac{3 sqrt{213}}{2} + frac{49}{2}} left(- sqrt{frac{3 sqrt{213}}{2} + frac{49}{2}} + 7right)$$
=
$$frac{1}{44} sqrt{3 sqrt{213} + 49} left(- 3 sqrt{426} + 49 sqrt{2}right)$$
=

1.61499867523486

$$y_{3} = – sqrt{frac{3 sqrt{213}}{2} + frac{49}{2}}$$
=
$$- frac{1}{2} sqrt{6 sqrt{213} + 98}$$
=

-6.81115109794150

$$x_{4} = frac{1}{11} left(-7 + sqrt{frac{3 sqrt{213}}{2} + frac{49}{2}}right) sqrt{frac{3 sqrt{213}}{2} + frac{49}{2}} left(sqrt{frac{3 sqrt{213}}{2} + frac{49}{2}} + 7right)$$
=
$$frac{1}{44} left(- 49 sqrt{2} + 3 sqrt{426}right) sqrt{3 sqrt{213} + 49}$$
=

-1.61499867523486

$$y_{4} = sqrt{frac{3 sqrt{213}}{2} + frac{49}{2}}$$
=
$$frac{1}{2} sqrt{6 sqrt{213} + 98}$$
=

6.81115109794150

x1 = -1.614998675234863
y1 = 6.811151097941495

x2 = -6.811151097941495
y2 = 1.614998675234863