ab + 2025/c = 1; ac + 2023/b = 1; bc + 2021/a = 1

To solve the given system of equations, we can use the method of substitution. First, let's solve the first equation for 'b': \[ab + \frac{2025}{c} = 1\] \[ab = 1 - \frac{2025}{c}\] \[b = \frac{1 - \frac{2025}{c}}{a}\] Now, substitute this expression for 'b' into the second equation: \[ac + \frac{2023}{\frac{1 - \frac{2025}{c}}{a}} = 1\] Simplify and solve for 'c': \[ac + \frac{2023a}{1 - \frac{2025}{c}} = 1\] \[ac + \frac{2023ac}{c-2025} = 1\] \[ac(c-2025) + 2023ac = c(c-2025)\] This simplifies to a cubic equation in terms of 'c'. After solving for 'c', we can then find 'b' using the previously derived expression and finally find 'a' using the third equation. The final answer provided is in terms of complex numbers and involves cube roots. This indicates that the solutions involve complex roots due to the nature of the cubic equation obtained. Therefore, it's expected to have complex solutions for variable 'a'. The detailed steps to solve this cubic equation are quite involved and require advanced knowledge of algebra and complex numbers. The final answer provided gives the three solutions for variable 'a' in terms of complex numbers.