X^(3)+x^(2)-x+1=\sqrt(3x+1)

To solve this equation, we can start by isolating the square root term on one side of the equation:

x^3 + x^2 - x + 1 = √(3x + 1)

Square both sides of the equation to eliminate the square root:

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

Expanding the left side of the equation:

x^6 + 2x^5 + x^4 - x^5 - 2x^4 - x^3 + x^4 + 2x^3 + x^2 - x^3 - 2x^2 - x + x^2 + 2x + 1 = 3x + 1

Combining like terms:

x^6 + x^5 - x^4 + x^3 - x^2 - x + 1 = 3x + 1

Rearranging the terms:

x^6 + x^5 - x^4 + x^3 - x^2 - 3x = 0

Factoring out an x:

x(x^5 + x^4 - x^3 + x^2 - x - 3) = 0

Now we have two possible solutions:

1) x = 0

2) x^5 + x^4 - x^3 + x^2 - x - 3 = 0

To solve the second equation, we can use numerical methods or approximation techniques.