Resposta:

[tex]\textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\sf{\sqrt{\left(x^2\:-\:144\right)}\:+\:\sqrt{\left(x^2\:-\:81\right)}\:=\:\sqrt{\left(2x^2\:-}\:9\right)}[/tex]

[tex]\sf{\left(\sqrt{\left(x^2\:-\:144\right)}\:+\:\sqrt{\left(x^2\:-\:81\right)}\right)^2\:=\:\left(\sqrt{\left(2x^2\:-}\:9\right)\right)^2}[/tex]

[tex]\sf{(x^2 - 144) +2\:.\:\sqrt{(x^2 - 144)\:.\:(x^2 - 81)} + (x^2 - 81 )= (2x^2 - 9)[/tex]

[tex]\sf{(2x^2 - 225) +2\:.\:\sqrt{(x^2 - 144)\:.\:(x^2 - 81)} = (2x^2 - 9)[/tex]

[tex]\sf{2\:.\:\sqrt{(x^2 - 144)\:.\:(x^2 - 81)} = 216}[/tex]

[tex]\sf{\left(2\:.\:\sqrt{(x^2 - 144)\:.\:(x^2 - 81)}\right)^2 = (216)^2}[/tex]

[tex]\sf{4\:.\:(x^2 - 144)\:.\:(x^2 - 81) = 46.656}[/tex]

[tex]\sf{4\:.\:(x^4 - 81x^2 -144x^2 + 11.664) = 46.656}[/tex]

[tex]\sf{4x^4 - 324x^2 -576x^2 + 46.656 = 46.656}[/tex]

[tex]\sf{4x^4 - 900x^2 = 0}[/tex]

[tex]\sf{4x^4 = 900x^2}[/tex]

[tex]\sf{x^2 = 225}[/tex]

[tex]\sf{x = \pm\:\sqrt{225}}[/tex]

[tex]\sf{x = \pm\:15}[/tex]

[tex]\boxed{\boxed{\sf{S = \{15;-15\}}}}[/tex]