1. **State the problem:** We are given the equation $$\frac{x^2}{2} + \frac{1}{x^2} - \frac{2}{x}$$ and told it can be rewritten as $$x^4 + ax^3 + bx^2 + cx + 2 = 0.$$ We need to find the values of $a$, $b$, and $c$. 2. **Rewrite the original expression:** Multiply both sides of the equation by $2x^2$ to clear denominators: $$2x^2 \times \left(\frac{x^2}{2} + \frac{1}{x^2} - \frac{2}{x}\right) = 2x^2 \times 0$$ which simplifies to $$x^4 + 2 - 4x = 0.$$ 3. **Compare with the given polynomial:** The rewritten polynomial is $$x^4 + 0 \cdot x^3 + 0 \cdot x^2 - 4x + 2 = 0.$$ 4. **Identify coefficients:** Comparing term by term with $$x^4 + ax^3 + bx^2 + cx + 2 = 0,$$ we get $$a = 0, \quad b = 0, \quad c = -4.$$ **Final answer:** $$a = 0, \quad b = 0, \quad c = -4.$$