26. [12] Determine the positive real value of $x$ for which
$$
\sqrt{2+A C+2 C x}+\sqrt{A C-2+2 A x}=\sqrt{2(A+C) x+2 A C} .
$$
Answer: 4 Note that if we have $\sqrt{a}+\sqrt{b}=\sqrt{a+b}$ for non-negative reals $a, b$, then squaring gives us that $2 \sqrt{a b}=0$, so that either $a=0$ or $b=0$.
Now, note that
$$
(2+A C+2 C x)+(A C-2+2 A x)=(2(A+C) x+2 A C) .
$$

Consequently, either $(2+A C+2 C x)$ or $(A C-2+2 A x)$ must be equal to 0 . However, we observe from the problems that both $A, C$, and $x$ must be non-negative, so $(2+A C+2 C x)>0$. As a result, we know that $A C-2+2 A x=0$, or that
$$
B=x=\frac{2-A C}{2 A} .
$$

If we solve our system of equations for $A, B, C$, we get that $B=4$.