I have got the following inequality
$|(a_{12}+a_{21}) x_1 - i (a_{12}-a_{21}) x_2 + (a_{11}-a_{22}) x_3 + (a_{11}+a_{21}) X| \le \sqrt{a_{11}^2 + |a_{21}|^2} + \sqrt{a_{22}^2 + |a_{12}|^2}$,
where $a_{12}=a_{21}^*$ are complex conjugates; and $a_{11}$ and $a_{22}$ are real coefficients. Also, $|\vec{x}| + |X|\le 1$. Here $\vec{x}=(x_1,x_2,x_3)$.
Problem: I need to solve for $x_1,x_2,x_3$ and $X$.
This is my first question on StackExchange. So please don't mind if you find something wrong in the way I am asking.
Edit: I have rewritten my question in a more simplified form which I just got.