(х-1)(х^2+х+1)-х^3-х^2=2х

Предыдущий
вопрос Следующий
вопрос

Let's simplify the given expression step by step:

(х-1)(х^2+х+1) = х(х^2+х+1) - 1(х^2+х+1) = х^3 + х^2 + х - х^2 - х - 1
= х^3 - 1

Now, substitute this back into the original expression:

х^3 - 1 - х^3 - х^2 = 2х

Since the х^3 terms cancel out, we are left with:

-1 - х^2 = 2х

Adding х^2 to both sides, we get:

-1 = 2х + х^2

Rearranging terms, we get:

х^2 + 2х + 1 = 0

This is a perfect square trinomial, which factors to:

(х + 1)^2 = 0

Therefore, the solution to the equation is:

х = -1