1. The problem is to solve the inequality $|x^4 + 2x^2 + 1| < 0$. 2. Recall that the absolute value $|A|$ of any expression $A$ is always greater than or equal to zero, i.e., $|A| \geq 0$ for all real $A$. 3. Since absolute values cannot be negative, the inequality $|x^4 + 2x^2 + 1| < 0$ has no solutions. 4. To confirm, note that $x^4 + 2x^2 + 1 = (x^2 + 1)^2 \geq 0$ for all real $x$, so its absolute value is also always non-negative. 5. Therefore, there is no $x$ such that $|x^4 + 2x^2 + 1| < 0$. Final answer: No solution.