Question

√(x^2 - 144) + √(x^2 - 81) = √(√2.x^2 - 9)

Alguem pode me ajudar?

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf{\sqrt{\left(x^2\:-\:144\right)}\:+\:\sqrt{\left(x^2\:-\:81\right)}\:=\:\sqrt{\left(2x^2\:-}\:9\right)}$

$\sf{\left(\sqrt{\left(x^2\:-\:144\right)}\:+\:\sqrt{\left(x^2\:-\:81\right)}\right)^2\:=\:\left(\sqrt{\left(2x^2\:-}\:9\right)\right)^2}$

$\sf{(x^2 - 144) +2\:.\:\sqrt{(x^2 - 144)\:.\:(x^2 - 81)} + (x^2 - 81 )= (2x^2 - 9)$

$\sf{(2x^2 - 225) +2\:.\:\sqrt{(x^2 - 144)\:.\:(x^2 - 81)} = (2x^2 - 9)$

$\sf{2\:.\:\sqrt{(x^2 - 144)\:.\:(x^2 - 81)} = 216}$

$\sf{\left(2\:.\:\sqrt{(x^2 - 144)\:.\:(x^2 - 81)}\right)^2 = (216)^2}$

$\sf{4\:.\:(x^2 - 144)\:.\:(x^2 - 81) = 46.656}$

$\sf{4\:.\:(x^4 - 81x^2 -144x^2 + 11.664) = 46.656}$

$\sf{4x^4 - 324x^2 -576x^2 + 46.656 = 46.656}$

$\sf{4x^4 - 900x^2 = 0}$

$\sf{4x^4 = 900x^2}$

$\sf{x^2 = 225}$

$\sf{x = \pm\:\sqrt{225}}$

$\sf{x = \pm\:15}$

$\boxed{\boxed{\sf{S = \{15;-15\}}}}$