This has always been difficult for me to understand. I always think that algebra's final solution must be a number.
I don't know why.
Take a look at this equation,
$$x_3+y_3+z_3=k$$
Someone can solve the $k$ in equation as follows,
$$3x + 3y + 3z = k$$
$$k = 3x + 3y + 3z$$
However, this has never been a solution for my brain because I never find a number.
I found an article claiming that the supercomputer solved the number for the equation.
So, this is not the only equation I have come across and I have found many.
So the name of this kind of equations are called as unsolvable problems? Does Academia have a better name than that?
Best Answer
This is a type of question where we express the variable of interest in terms of the other variables. Typically, we isolate the variable on one side.
The implication of this is that if the other variables' values are known to us, then we can find the corresponding value for our variable of interest. With the other variable not known, $k$ indeed remains unknown.
Another example: Solve for $x$ if $ax^2+bx+c=0$.
The general solution is $$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$$
Whenever you know $a,b,c$, you identify your $x$. A single formula can be used to solve all the quadratic equation.