82*. Find the value of $x$ for which the expression

$$
(a+b-x)^{2}+(b+c-x)^{2}+(c+a-x)^{2}
$$

becomes a perfect square.
Given. Denoting $(a+b-x)^{2}=A, \quad(b+c-x)^{2}=B$, $(c+a-x)^{2}=C$, and applying the condition obtained in the previous problem, we get: $A C=\left(\frac{B}{2}\right)^{2}$. Substituting the values of $A, B$ and $C$ and solving the resulting equation with respect to $x$:

$$
x=2 a \pm \sqrt{(a-b)^{2}+(a-c)^{2}}
$$