(Sqrt {10} - sqrt {2}) ^ 2 Zjednodušené na b-c sqrt {5}?

odpoveď:

Áno

vysvetlenie:

# (sqrt10 - sqrt2) ^ 2 #

# = (sqrt10 - sqrt2) (sqrt10 - sqrt2) # FOIL

# = sqrt10 * sqrt10 + sqrt10 * (- sqrt2) + sqrt10 * (- sqrt2) + (- sqrt2) * (- sqrt2) #

# = 10 - 2sqrt10sqrt2 + 2 #

# = 12 - 2sqrt10sqrt2 #

# = 12 - 2sqrt5 * sqrt2 * sqrt2 # #lArr "pretože:" sqrt10 = sqrt2 * sqrt5 #

# = 12 - 2sqrt5 * 2 #

# = 12 - 4sqrt5 #

# = 4 (3 - sqrt5) #