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(x+y)^2=36; x^2+y^2=a

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       2     
(x + y)  = 36
$$\left(x + y\right)^{2} = 36$$
 2    2    
x  + y  = a
$$x^{2} + y^{2} = a$$
x^2 + y^2 = a
Rapid solution
$$a_{1} = - 2 y \left(6 - y\right) + 36$$
=
$$2 y \left(y - 6\right) + 36$$
=
36 - 2*y*(6 - y)

$$x_{1} = 6 - y$$
=
$$6 - y$$
=
6 - y
$$a_{2} = - 2 y \left(- y - 6\right) + 36$$
=
$$2 y \left(y + 6\right) + 36$$
=
36 - 2*y*(-6 - y)

$$x_{2} = - y - 6$$
=
$$- y - 6$$
=
-6 - y