Prosimo, rešite q 70?

Odgovor:

Odgovor je #option (2) #

Pojasnilo:

Potrebujemo

# (a + b) ^ 3 = a ^ 3 + 3a ^ 2b + 3ab ^ 2 + b ^ 3 = a ^ 3 + b ^ 3 + 3ab (a + b) #

Let # a = 8 + x #

in

# b = 8-x #

Torej, # a ^ (1/3) + b ^ (1/3) = 1 #

Cubing obe strani

# (a ^ (1/3) + b ^ (1/3)) ^ 3 = 1 ^ 3 #

# a + b + 3a ^ (1/3) b ^ (1/3) (a ^ (1/3) + b ^ (1/3)) = 1 #

Zato, # a + b + 3a ^ (1/3) b ^ (1/3) = 1 #

# 8 + x + 8-x + 3 (8 + x) ^ (1/3) (8-x) ^ (1/3) = 1 #

# 16 + 3 (64-x ^ 2) ^ (1/3) = 1 #

# 3 (64-x ^ 2) ^ (1/3) = - 15 #

# (64-x ^ 2) ^ (1/3) = - 5 #

Cubing obe strani

# 64-x ^ 2 = -125 #

# x ^ 2-189 = 0 #

Produkt korenin te kvadratne enačbe je #=-189#

Odgovor je #option (2) #

Odgovor:

# -189#.

Pojasnilo:

Podana eqn. je, #root (3) (8 + x) + koren (3) (8-x) = 1 ………… (zvezda) #.

Cubing, # (root (3) (8 + x) + koren (3) (8-x)) ^ 3 = 1 ^ 3 = 1 #.

#:. (koren (3) (8 + x)) ^ 3+ (koren (3) (8-x)) ^ 3 #

# + 3 * (korenski (3) (8 + x)) * (korenski (3) (8-x)) ((korenski (3) (8 + x) + korenski (3) (8-x)) = 1 #.

#:. (8 + x) + (8-x) + 3 * koren (3) (64-x ^ 2) (1) = 1 ………… ker, (zvezda) #.

#:. 3 * koren (3) (64-x ^ 2) (1) = 1-16 = -15 #.

#:. root (3) (64-x ^ 2) = - 5.

#:. {root (3) (64-x ^ 2)} ^ 3 = (- 5) ^ 3 #.

#:. 64-x ^ 2 = -125 #.

#:. -x ^ 2 = -189 #.

# ali, x ^ 2-189 = 0 ali, x ^ 2-0x-189 = 0 #.

#:. "Proizvod korenin" = - 189/1 = -189 #.

Torej, prava možnost je #(2): -189#.