Løs venligst venligst q4 og 5?

Svar:

# N = 0 #

Forklaring:

Spørgsmål 4:

Givet:

# N = sqrt (6 + sqrt11) + sqrt (6-sqrt11) -sqrt22 #

Lade, #sqrt (6 + sqrt11) = sqrtp + sqrtq #

Derefter, #sqrt (6-sqrt11) = sqrtp-sqrtq #

Squaringand tilføje

# (6 + sqrt11) + (6-sqrt11) = p + q + 2sqrt (pq) + p + q-2sqrt (pq) #

# 12 = 2 (p + q) #

# P + q = 12/2 = 6 #

# P + q = 6 #

Kvadrering og subtraktion

# (6 + sqrt11) - (6-sqrt11) = (p + q + 2sqrt (pq)) - (p + q-2sqrt (pq)) #=

# 2sqrt11 = 4sqrt (pq) #

#sqrt (pq) = (2sqrt11) / 4 = sqrt (11) / 2 #

Squaring

# Pq = 11/4 = 2,75 #

# X ^ 2-Sumx + Produkt = 0 #

# X ^ 2-6x + 2,75 = 0 #

# X ^ 2-5.5x-0,5x + 2,75 = 0 #

#x (x-5.5) -0.5 (x-5,5) = 0 #

# (X-5,5) (x-0,5) = 0 #

# x-5,5 = 0tox = 5,5 #

# x-0,5 = 0tox = 0,5 #

En af rødderne kan være p, andre bliver q.

Dermed, #sqrt (6 + sqrt11) = sqrt5.5 + sqrt0.5 #

Den følger det

#sqrt (6-sqrt11) = sqrt5.5-sqrt0.5 #

Nu, #sqrt (6 + sqrt11) + sqrt (6-sqrt11) -sqrt22 = sqrt5.5 + sqrt0.5 + sqrt5.5-sqrt0.5-sqrt22 #

# = 2sqrt5.5-sqrt22 #

# = Qrt4sqrt5.5 = sqrt22 #

# = sqrt (4xx5.5) -sqrt22 #

# = Sqrt22-sqrt22 #

#=0#

Dermed,

# N = 0 #