suma directa y sistema cúbic

x^{3} + y^{3} = x + p
x^{3} + y^{3} = y + q
x + y = m


(1/4)·( x [+] y )^{3} = x + p
(1/4)·( x [+] y )^{3} = y + q
x + y = m


(1/4)·( (m/2) [+] (m/2) )^{3} = x + p
(1/4)·( (m/2) [+] (m/2) )^{3} = y + q
x + y = m


(m^{3}/4) = x + p
(m^{3}/4) = y + q
x + y = m


(m^{3}/4) + (-p) = x
(m^{3}/4) + (-q) = y
x + y = m


(m^{3}/2) = m + (p[+]q)
m^{3} = 2m + 2·(p[+]q)


m = ( (1/2)( 2(p[+]q) + ( 4(p[+]q)^{2}+(32/27) )^{(1/2)} ) )^{(1/3)} + ...
... ( (1/2)( 2(p[+]q) + (-1)( 4(p[+]q)^{2}+(32/27) )^{(1/2)} ) )^{(1/3)}


m^{3} = 2·(p[+]q) + 2m


(1/32)·(m^{3})^{3} = ...
... (1/32)·( 8·(p[+]q)^{3}+3·( 4·(p[+]q)^{2}·(2m) )+3·( 2·(p[+]q)·(4m^{2}) )+8m^{3} )


(-1)(3/16)·(p[+]q)·(m^{3})^{2} = ...
... (-1)(3/16)·(p[+]q)·( 4·(p[+]q)^{2}+2·2·(p[+]q)·(2m)+4m^{2} )


(3/4)·(1/2)·(p[+]q)^{2}·(m^{3}) = ...
... (3/8)·(p[+]q)^{2}·( 2·(p[+]q)+(2m) )