Hoe waardeert u 108 m ^ 3 - 500?

Antwoord:

# = (3m-5) (6m + 5 (1 + sqrt (3) i)) (6m + 5 (1-sqrt (3) i)) #

Uitleg:

#108 = 4 * 27 = 4 * 3^3#

#500 = 4 * 125 = 4 * 5^3#

#"Dus we hebben"#

# 4 ((3m) ^ 3 - 5 ^ 3) #

# "Nu passen we" a ^ 3-b ^ 3 = toe (a-b) (a ^ 2 + ab + b ^ 2) "#

# = 4 (3m - 5) (9m ^ 2 + 15m + 25) #

# "De kwadratische factor kan ook worden meegerekend in factoren" #

# "met complexe getallen als volgt:" #

# "schijf:" 15 ^ 2 - 4 * 9 * 25 = -675 = -27 * 25 = -27 * 5 ^ 2 #

# => m = (-15 uur 5 sqrt (27) i) / 18 #

# => m = (-5 pm 5 sqrt (3) i) / 6 #

# => m = - (5/6) (1 pm sqrt (3) i) #

# => 9 (m + (5/6) (1 + sqrt (3) i)) (m + (5/6) (1 - sqrt (3) i)) #

# "Dus we krijgen" #

# 36 (3m - 5) (m + (5/6) (1 + sqrt (3) i)) (m + (5/6) (1-sqrt (3) i)) #

# = (3m-5) (6m + 5 (1 + sqrt (3) i)) (6m + 5 (1-sqrt (3) i)) #