Odgovor:
Jih ni. Korenine so # = + - 1.7078 + -1.4434 #, skoraj.
Pojasnilo:
Enačbo lahko reorganiziramo kot
# (x ^ 2--5 / 6) ^ 2 = - (5 / 6sqrt35) ^ 2 = i ^ 2 (5 / 6sqrt35) ^ 2 # kar daje
# x ^ 2 = 5/6 (1 + -isqrt35) #. In tako, # x = (5 (1/6 + -isqrt35 / 6)) ^ (1/2) #
# = sqrt5cis ((k360 ^ o + -80,40 ^ o) / 2), k = 0, 1 #, z uporabo De Moivre
izrek
# = sqrt5 (cos 40.203 ^ 0 + -i sin 40.203 ^ 0) # in.
# sqrt5 (cos 220.203 ^ 0 + -i sin 220.203 ^ 0) #
# = 1.7078 + -i1.4434 in -1.70755 + -1.4434 #
# = + - 1.7078 + -1.4434 #