Kakšen je pravilen odgovor?

Odgovor:

# (A) - (sqrt (7) +7) / 3 #

Pojasnilo:

# "Pomnožite števec in imenovalec z" 1 + sqrt (7) ":" #

# = (2 sqrt (7) (1 + sqrt (7))) / ((1-sqrt (7)) (1 + sqrt (7))) #

# "Zdaj se uporablja" (a-b) (a + b) = a ^ 2-b ^ 2 ":" #

# = (2 sqrt (7) (1 + sqrt (7))) / (1-7) #

# = (2 sqrt (7) (1 + sqrt (7))) / - 6

# = - (sqrt (7) (1 + sqrt (7))) / 3 #

# = - (sqrt (7) +7) / 3 #

# => "Odgovor (A)" #

Odgovor:

Glej spodaj.

Pojasnilo:

# (2 sqrt7) / (1-sqrt7) = (2 sqrt7) / (1-sqrt7) ((1 + sqrt7) / (1 + sqrt7)) = (2sqrt7 + 14) / (1-7) = - (sqrt7-7) / 3 #

Odgovor:

# A #

Pojasnilo:

Da bi našli odgovor, moramo racionalizirati imenovalec.

Dobili smo:

# (2sqrt (7)) / (1-sqrt (7)) #

Moramo pomnožiti vrh in dno # 1 + sqrt (7) # ker bo izničil kvadratni koren na dnu.

# (2sqrt (7)) / (1-sqrt (7)) * (1 + sqrt (7)) / (1 + sqrt (7)) = (2sqrt (7) (1 + sqrt (7))) / ((1-sqrt (7)) (1 + sqrt (7))) = (2sqrt (7) +14) / (1 + sqrt (7) -sqrt (7) -7) = (2sqrt (7) + 14) / (- 6) = - (2sqrt (7) +14) / 6 = - (sqrt (7) +7) / 3- = A #