How can I find the X nature from this circuit?
I am a little confused by your question, so I will state my assumptions clearly:


\$R2 = 1k\Omega\$, all other values are unknown
The X component is either a capacitor or an inductor. If it is a inductor, it has impedance \$Z(s) = sL\$. If it is a capacitor, it has impedance \$Z(s) = 1/(sC)\$
No funny business: there are no negative resistances, capacitances or inductances in the circuit


Now you can simply use algebra and Kirchoff's laws. Before doing the math it is hard to know if there is one, many or no solution.

This is the brute force approach, and it will work. You should give it a try. However, a experienced engineer may notice a few things that might make solving the equations a lot easier:


You can easily run a "sanity-check" in this circuit with \$ \omega = 0\$ and \$ \omega = \infty \$
Notice this looks like a Wheatstone bridge circuit. As such, you should pay attention to the ratio between impedances of R2 and R3, and between R1 and X. This tells you something about the number of solutions this problem can have.