Question

considere x=$\sqrt{4+2 \sqrt{3} } - \sqrt{4-2 \sqrt{3} } .$. Com base no valor de $x^{2}$, é correto afirmar que x é:

a) irracional positivo.
b) irracional negativo.
c) zero.
d) inteiro positivo.
e) inteiro negativo.

Answer 1

Oi Rafael.


Organizando e resolvendo a equação:


$\mathsf{x=\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}}\\\\\mathsf{x^2=(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}})^2}\\\\\mathsf{x^2=4+2\sqrt{3}-2\sqrt{(4+2\sqrt{3})\cdot(4-2\sqrt{3})}+4-2\sqrt{3}}\\\\\mathsf{x^2=8-2\sqrt{16-8\sqrt{3}+8\sqrt{3}-4\cdot 3}}\\\\\mathsf{x^2=8-2\sqrt{16-12}}\\\\\mathsf{x^2=8-2\sqrt{4}}\\\\\mathsf{x^2=8-2\cdot2}\\\\\mathsf{x^2=8-4}\\\\\boxed{\mathsf{x^2=4}}$

Resposta (d).


Dúvidas? comente.