Los alstublieft q57 op?

Antwoord:

Het antwoord is #option (4) #

Uitleg:

ik gebruik #een#, # B # en # C # in plaats van # Alpha #, # Beta # en #gamma#

# A + b + c = 2 #, # A ^ 2 + b + c ^ 2 ^ 2 = 6 # en

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

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

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

#=>#, # Ab + BC + ca = (6/4) / 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 #

Maar,

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

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

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

daarom

# A ^ 2b ^ 2 + b ^ 2c ^ 2 + c ^ 2a ^ 2 = 4/1 = -3 #

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

Het antwoord is #option (4) #