Rešite (x-2) ^ 3 = x ^ 3 - 2?

Rešite (x-2) ^ 3 = x ^ 3 - 2?
Anonim

Odgovor:

1

Pojasnilo:

Glede,# (x-2) ^ 3 = x ^ 3-2 #

#rArr x ^ 3-3x ^ 2. 2 + 3x.2 ^ 2-2 ^ 3 = x ^ 3-2 #

#rArr x ^ 3-x ^ 3-6x ^ 2 + 12x-8 + 2 = 0 #

#rArr -6x ^ 2 + 12x-6 = 0 #

#rArr -6 (x ^ 2-2x + 1) = 0 #

#rArr x ^ 2-2x + 1 = 0 #razdelite obe strani z -6

#rArr (x-1) ^ 2 = 0 #

#rArr x-1 = 0 #kvadriranje obeh strani

#rArr x = 1 #