2) (x+1)² + √(x + 1)³ + √(2x + 1)³ = 3

To solve the equation

\[
2(x+1)² + \sqrt{(x+1)³} + \sqrt{(2x+1)³} = 3,
\]

let's define some substitutions to simplify our work:

1. Let \( y = x + 1 \). Then the equation becomes:
\[
2y² + \sqrt{y³} + \sqrt{(2(y-1)+1)³} = 3
\]
which simplifies to:
\[
2y² + \sqrt{y³} + \sqrt{(2y-1)³} = 3.
\]

2. The equation now is:
\[
2y² + y^{3/2} + (2y-1)^{3/2} = 3.
\]

Now, you can solve this equation either by analytical methods or by numerical methods (like graphing or using a numerical solving approach).

### Steps to Numerical Solution:
1. **Graphing:** Plot the left side \( f(y) = 2y² + y^{3/2} + (2y-1)^{3/2} \) and \( y = 3 \) to find intersections.

2. **Trial values:** Substitute various values for \( y \) to find solutions roughly.

3. If using numerical methods or a calculator, find \( y \) such that \( f(y) = 3 \).

After finding \( y \), revert back to \( x \) using \( x = y - 1 \) to obtain the final solution.

If you need help with graphing or approximation, please let me know!