suma directa y sistema cuadrátic

x^{2} + y^{2} = x + p
x^{2} + y^{2} = y + q
x + y = m


(1/2)·( x [+] y )^{2} = x + p
(1/2)·( x [+] y )^{2} = y + q
x + y = m


(1/2)·( (m/2) [+] (m/2) )^{2} = x + p
(1/2)·( (m/2) [+] (m/2) )^{2} = y + q
x + y = m


(m^{2}/2) = x + p
(m^{2}/2) = y + q
x + y = m


(m^{2}/2) + (-p) = x
(m^{2}/2) + (-q) = y
x + y = m


m^{2} = m + (p [+] q)


m = (1/2)·( 1+( 1+4·(p[+]q) )^{(1/2)} )


x + y = m
(1/4)·( 1+2·( 1+4·(p[+]q) )^{(1/2)}+(1+4·(p[+]q)) ) + (-1)·(p[+]q) = ...
...  (1/2)·( 1+( 1+4(p[+]q) )^{(1/2)} )


(1/2)·m^{4} + (-1)·(p[+]q)·m^{2} + (1/2)·(p[+]q)^{2} = (1/2)·m^{2}
(1/32)·( 1 + 4·( 1+4·(p[+]q) )^{(1/2)} + 6·( 1+4·(p[+]q) ) + ...
... 4·(1+4·(p[+]q))·( 1+4·(p[+]q) )^{(1/2)} + (1+4·(p[+]q))^{2} ) = ...
... (1/8)·( 1+2·( 1+4·(p[+]q) )^{(1/2)}+(1+4·(p[+]q)) )