Molimo riješite q57?

Odgovor:

Odgovor je #option (4) #

Obrazloženje:

koristim # S #, # B # i # C # umjesto #alfa#, #beta# i #gama#

# A + b + c = 2 #, # A ^ 2 + b + c ^ 2 ^ 2-6 # i

# A ^ 3 + b + c ^ 3 ^ 3 = 8 #

#=>#, # (A + b + c) = 2 ^ 2 ^ 2-4 #

#=>#, # A ^ 2 + b + c ^ 2 ^ 2 + 2 (ab + bc + ca) = 4 #

#=>#, # Ab + bc + ca = (4-6) / 2 = -1 #

#=>#, # (Ab + bc + ca) ^ 2 = (- 1) ^ 2-1 #

#=>#, # A ^ 2b ^ 2 + b ^ 2c ^ 2 + C ^ 2a ^ 2 + 2ABC (ab + bc + ca) = 1 #

#=>#, # A ^ 2b ^ 2 + b ^ 2c ^ 2 + C ^ 2a ^ 2 + 2ABC (1) = 1 #

#=>#, # A ^ 2b ^ 2 + b ^ 2c ^ 2 + C ^ 2a ^ 2-2abc = 1 #

Ali,

# A ^ 3 + b + c ^ 3 ^ 3-3abc = (a + b + c) (a + b ^ 2 ^ 2 + c ^ 2- (ab + bc + ca)) *

#=>#, # 8-3abc = 2 * (6 + 1) #

#=>#, # Abc = (8-14) / 3 = -2 #

Stoga, # A ^ 2b ^ 2 + b ^ 2c ^ 2 + C ^ 2a ^ 2-1-4--3 #

#=>#, # (A + b ^ 2 ^ 2 + c ^ 2) ^ 2 = 36 #

#=>#, # A ^ 4 + b + c ^ 2 ^ 4 + 2 (a ^ 2b ^ 2 + b ^ 2c ^ 2 + a ^ 2c ^ 2) = 36 #

#=>#, # A ^ 4 + b + c ^ 2 ^ 4 = 36-2 (-3) = 42 #

Odgovor je #option (4) #