Answer
$\sqrt (x+a)+\sqrt (x-a)=\sqrt 2\sqrt (x+6)$
If $a=0, x=6$
If $a\gt0, x=\sqrt (36+a^{2})$
Work Step by Step
$\sqrt (x+a)+\sqrt (x-a)=\sqrt 2\sqrt (x+6)$
Domain: $x>or=a$
Square both side:
$(\sqrt (x+a)+\sqrt (x-a))^{2}=2(x+6)$
$x+a+2(\sqrt (x+a)\times\sqrt (x-a))+x-a=2x+12$
$2x+2(\sqrt (x+a)\times\sqrt (x-a))=2x+12$
$(\sqrt (x+a)\times\sqrt (x-a))=6$
Square both side:
$(x+a)\times(x-a)=36$
$x^{2}-a^{2}=36$
If $a=0, x=6$ or $x=-6 (reject)$
If $a\gt0, x=\sqrt (36+a^{2})$ or $x=-\sqrt (36+a^{2}) (reject)$
