[Daily puzzle] Tricky system of equations \ stacker news ~science

Here is a tricky one to keep you busy while waiting for the AP to announce the election results...

Can you solve the following system of equations for real variables

and

where

and

are distinct real numbers?

Previous iteration: #753021 (visual and written answers in #753251 and #753272, respectively).

All that has to equal to

, so we get a system of equations:

Which if we solve gives us:

By symmetry it's easy to show that this solutions works for all three of the above equations.

Correct!

I'm not a mathematician, but if I studied it maybe I could understand it a little.

Never too late~~

You can click through to earlier iterations, I've posted easier ones that rely on some logical reasoning rather than equations.

That's right, I also want to be good at mathematics, I have to try and not be late in learning mathematics.

I don't want to spoil anyone's fun, but the answer is pretty obvious on this one....

I'm pretty sure you know that I know. 😏

I'm only 42% sure.