Question

identifique a alternativa que corresponde ao valor da expressao 1/√2 + 1/√18 -1/√8
A:√3/6
B:√12
C: -10/ √288
D: -5√12/12
E: 5√2/12

Answer 1

Resposta:

A alternativa correta é a letra E.

Explicação passo-a-passo:

Se estiver com problemas para visualizar a resposta no app, tente usar o navegador acessando https://brainly.com.br/tarefa/40170340

$x=\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{18}}-\dfrac{1}{\sqrt{8}}\\\\\\x=\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{9\;.\;2}}-\dfrac{1}{\sqrt{4\;.\;2}}\\\\\\x=\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{9}\;.\;\sqrt{2}}-\dfrac{1}{\sqrt{4}\;.\;\sqrt{2}}\\\\\\x=\dfrac{1}{\sqrt{2}}+\dfrac{1}{3\sqrt{2}}-\dfrac{1}{2\sqrt{2}}$

$m.m.c\;de\;\sqrt{2},3\sqrt{2}\;e\;2\sqrt{2}=\begin{array}{ccc|c}\sqrt{2}&3\sqrt{2}&2\sqrt{2}&\sqrt{2}\\1&3&2&2\\1&3&1&3\\1&1&1&\end{array}\right]\\\\\\m.m.c\;de\;\sqrt{2},3\sqrt{2}\;e\;2\sqrt{2}=2\;.\;3\;.\;\sqrt{2}\\\\\\m.m.c\;de\;\sqrt{2},3\sqrt{2}\;e\;2\sqrt{2}=6\sqrt{2}$

Portanto,

$x=\dfrac{6+2-3}{6\sqrt{2}}\\\\\\x=\dfrac{8-3}{6\sqrt{2}}\\\\\\x=\dfrac{5}{6\sqrt{2}}\\\\\\x=\dfrac{5}{6\sqrt{2}}\;.\;\dfrac{6\sqrt{2}}{6\sqrt{2}}\\\\\\x=\dfrac{5\;.\;6\sqrt{2}}{(6\sqrt{2})^2}\\\\\\x=\dfrac{30\sqrt{2}}{6^2\;.\;(\sqrt{2})^2}\\\\\\x=\dfrac{30\sqrt{2}}{36\;.\;2}\\\\\\\boxed{x=\dfrac{30\sqrt{2}}{72}=\dfrac{15\sqrt{2}}{36}=\dfrac{5\sqrt{2}}{12}} \quad \rightarrow \quad \mathbf{letra\;E}$