Relations between numbers taken three at a time [closed]

Let's have the following numbers.

$$(5i+\frac{1}{2})$$, $$(2i+3)$$, $$(\frac{-101}{8})$$, $$(7i+4)$$, $$(5i+1)$$, $$\frac{(40i-97)}{8}$$.

How are these numbers related when taken three at a time? Operations allowed + - x ÷ ^

HINT: The three numbers, when chosen correctly, will solve this equation: $$x^3=a^2-b^2$$

There is only one solution.

• This looks to be another "guess what I'm thinking" problem. Three are probably infinitely many relationships one could draw. – bobble Mar 1 at 0:27
• When the numbers are chosen correctly, three at a time, (no more than three numbers) there is only one answer. – Vassilis Parassidis Mar 1 at 0:32
• That's not a hint, it's the problem statement. Without telling us what equation to solve, this isn't a puzzle. It's a guessing game. – bobble Mar 1 at 2:27
• @ bobble. Choose the three numbers with denominators then you can answer the question. – Vassilis Parassidis Mar 1 at 2:41

$$(2i+3)+(5i+1)+\frac{(40i-97)}{8} = \left(5i+\frac{1}{2}\right) + (7i+4) + \left(\frac{-101}{8}\right)$$