Have any ways to reverse from LHS variables by RHS variables of a group of equations?
For example:
How can I reverse those equations to new equations set likes:
What are those functions look likes?
Thanks
Mathematica spits out 8 solutions, but they are extraordinarily long. I'm not even going to attempt to post them here, as they are multi-line solutions. Algebraically, though, there's nothing more complicated than powers and square roots and fractions, and such. I would try to find someone who has Mathematica, and enter the following command:
Simplify[Solve[{a^2 + 2b c == x, b^2 + 2a c == y, c^2 + 2a b == z}, {a, b, c}]].
That should do it.
Let be a complex cube root of unity. Then
Let be one of the two square roots of , and similarly let and Thus there are eight possible choices for the triple of complex numbers
Then , and
Since , it follows that , and
That gives the solution in the neat form
Of course, if you write X, Y and Z in terms of x, y and z, it won't look quite so neat. But I reckon that I can claim Opalg: 1, Mathematica: 0.
Many thank for your works!
It's great for having steps to the solution even I don't understand completely. And I never thought that how apply cube root of unity to solve this issue so I've difficult to digest these steps but still thanks.
I treats above question similar as just a square root to a number consisted with {x,y,z}.