<s>[INST] Roots in equation In the equation
$\sqrt{x-2} - \sqrt{6x-11} + \sqrt{x+3} =0$
I got the roots of $x$ being $6$ and $7\sqrt{3}$.
Considering the graph shows only $6$ as being a valid solution, how should I go as figuring this out in the equation itself?
 [/INST] Let $x=7\sqrt 3$ into $$\sqrt{x-2} - \sqrt{6x-11} + \sqrt{x+3} $$ and you get $$ \sqrt{x-2} - \sqrt{6x-11} + \sqrt{x+3} \approx -0.7869 \ne 0$$
Thus $x=7\sqrt 3$ is not a solution.
</s>