Question

(х+1)(х²+2)+(х+2)( х²+1)=2

Answer 1

(х+1)(х²+2)+(х+2)( х²+1)=2

2х^3+3x+3x^2+2=0

(x+1)(2x^2+x+2)=0

x+1=0

2x^2+x+2=0

x=-1

x ∈R

Ответ : х = -1

Answer 2

To solve the equation, we need to expand the expressions and then simplify the equation. Let's start by expanding the expressions:

1. Expand (х+1)(х²+2): (х+1)(х²+2) = х * х² + х * 2 + 1 * х² + 1 * 2 = х³ + 2х + х² + 2

2. Expand (х+2)(х²+1): (х+2)(х²+1) = х * х² + х * 1 + 2 * х² + 2 * 1 = х³ + х + 2х² + 2

Now, let's rewrite the equation with the expanded expressions:

(х³ + 2х + х² + 2) + (х³ + х + 2х² + 2) = 2

Combine like terms:

2х³ + 3х² + 3х + 4 = 2

Now, let's move all terms to one side of the equation:

2х³ + 3х² + 3х + 4 - 2 = 0

Simplify:

2х³ + 3х² + 3х + 2 = 0

This equation is a cubic equation in terms of x. To find the solutions for x, we can use numerical methods or factorization techniques. However, as it stands, it does not seem to have simple integer solutions. If you have specific values for x that need to satisfy the equation, please provide them, and I can help verify whether they are solutions or not.