Question

\(\large\text{This is out of the syllabus! random question no. 1}\)!! :D

If
\(\large x=\sqrt{11-2yz}\) \(\large y=\sqrt{12-2xz}\) \(\large z=\sqrt{13-2xy}\)

and all solutions are real numbers, then \(\large x+y+z=~?\)

Answer 1

\[x^2+y^2+z^2=11+12+13-2(yz+xz+xy)\\x^2+y^2+z^2+2(yz+xz+xy)=36\\(x+y+z)^2=36\\x+y+z=6\]

Answer 2

Haha, nice, that was sure an easy one for you :P