theorem :: POLYEQ_4:19

for x, y, a, b, p being Real
for n being Element of NAT st (a * (x |^ n)) + (b * (y |^ n)) = p & x * y = 0 & n is even & n >= 1 & p / b > 0 & p / a > 0 & a * b <> 0 & not ( x = 0 & y = n -root (p / b) ) & not ( x = 0 & y = - (n -root (p / b)) ) & not ( x = n -root (p / a) & y = 0 ) holds
( x = - (n -root (p / a)) & y = 0 )