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

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

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

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 $\large x+y+z=~?$

anonymous · Answer

$$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$$

zepp · Answer

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