1. The problem is to find the number of roots of the equation $$\left(x^3 - \frac{1}{x}\right)^2 = 0$$. 2. Since the square of an expression equals zero, that expression itself must be zero: $$x^3 - \frac{1}{x} = 0$$. 3. Multiply both sides by $x$ (not zero) to clear the denominator: $$x^4 - 1 = 0$$. 4. Rewrite as $$x^4 = 1$$. 5. The equation $x^4 = 1$ has solutions that are the fourth roots of unity. 6. The fourth roots of unity satisfy $$x = e^{i\frac{2\pi k}{4}}$$ for $k=0,1,2,3$, which correspond to values $$x = 1, i, -1, -i$$. 7. There are 4 distinct roots of the equation. 8. Check none of the roots make the original expression undefined. Since $x=0$ would make $\frac{1}{x}$ undefined, but zero is not a root, all good. 9. Hence the total number of roots is 4. 10. The closest answer choice among (ক) 3, (খ) 6, (গ) 10 is not listed exactly; however, strictly speaking, the total roots are 4.