Racionalizirajte (3-) 5) ÷ (3 + 5) Ali lahko to razumete?

Odgovor:

Opomba: imenovalec lahko racionaliziramo le v tem primeru.

# (3-sqrt (5)) div (3 + sqrt (5)) = barva (rdeča) ("" (1- (3sqrt (5)) / 2) #

Pojasnilo:

# (3-sqrt (5)) div (3 + sqrt (5)) #

#color (white) ("XXX") = (3-sqrt (5)) / (3 + sqrt (5)) #

Množenje števca in imenovalca s konjugacijo imenovalca:

#color (white) ("XXX") = (3-sqrt (5)) / (3 + sqrt (5)) xx (3-sqrt (5)) / (3-sqrt (5)) #

#barva (bela) ("XXX") (3 ^ 2-2 * 3 * sqrt (5) + (sqrt (5)) ^ 2) / (3 ^ 2- (sqrt (5) ^ 2) #

#barva (bela) ("XXX") = (9-6sqrt (5) +5) / (9-5) #

#color (bel) ("XXX") = (4-6sqrt (5)) / 4 #

#barva (bela) ("XXX") = 1- (3sqrt (5)) / 2 #