suma directa y ecuacions cuártiques

x^{4}+y^{4} = k
(1/8)·( x[+]y )^{4} = k
( x[+]y )^{4} = 8k
( x[+]y ) = 8^{(1/4)}·k^{(1/4)}


x = (4/8^{(3/4)})·k^{(1/4)}
y = (4/8^{(3/4)})·k^{(1/4)}


x^{4}+y^{4} = (x+y)
(1/8)·( x[+]y )^{4} = (x+y)
( x[+]y )^{4} = 8·(x+y)
( x[+]y ) = 8^{(1/4)}·(x+y)^{(1/4)}


x = 1
y = 1


x^{4}+y^{4} = (x+y)^{3}
(1/8)·( x[+]y )^{4} = (x+y)^{3}
( x[+]y )^{4} = 8·(x+y)^{3}
( x[+]y ) = 8^{(1/4)}·(x+y)^{(3/4)}


x = 4
y = 4