Question

A raiz da equação √x+4 + √x-4 / √x+4 - √x+4 =2 pertence ao intervalo

Answer 1

Vamos substituir:

$a= \sqrt{x+4} \rightarrow a^2=x+4\\ b= \sqrt{x-4} \rightarrow b^2=x-4\\ \\ \frac{a+b}{a-b}=2 \\ \\ a+b=2(a-b)\\ (a+b)^2=[2(a-b)]^2\\ a^2+2ab+b^2=4(a^2-2ab+b^2)\\ a^2+2ab+b^2=4a^2-8ab+4b^2\\ 3a^2-10ab+3b^2=0\\ 3(x+4)-10 \sqrt{x^2-16}+3(x-4)=0 \\ 3x+12-10\sqrt{x^2-16}+3x-12=0\\ 6x=10\sqrt{x^2-16}\\ 36x^2=100(x^2-16)\\ 36x^2=100x^2-1600\\ 64x^2=1600\\ x^2=25\\ \boxed{x=5}$