Question

unifor-ce simplificando-se a expressão [(2/√2-1)÷√2/2]x(√2/2+1), obtém-se:a)-√2b)-1c)1d)√2e)2Gabarito: c

Answer 1

$\left [\left( \dfrac{2}{ \sqrt{2}-1} \right ): \dfrac{ \sqrt{2}}{2}\right]* \left(\dfrac{ \sqrt{2}}{2}+1\right )= \\ \\ \\ \left [ \dfrac{2*2}{ (\sqrt{2}-1)* \sqrt{2} }\right]* \left(\dfrac{ \sqrt{2}+2}{2}\right )= \\ \\ \\ \left [ \dfrac{4}{ \sqrt{2}^2- \sqrt{2} }\right]* \left(\dfrac{ \sqrt{2}+2}{2}\right )= \\ \\ \\ \left [ \dfrac{4}{ 2- \sqrt{2} }\right]* \left(\dfrac{ \sqrt{2}+2}{2}\right )=$

$\left [ \dfrac{4}{ (2- \sqrt{2}) }* \dfrac{(2+ \sqrt{2})}{(2+ \sqrt{2})} \right]* \left(\dfrac{ \sqrt{2}+2}{2}\right )= \\ \\ \\ \left [ \dfrac{8+4 \sqrt{2} }{ (2)^2- (\sqrt{2})^2 }} \right]* \left(\dfrac{ \sqrt{2}+2}{2}\right )= \\ \\ \\ \left [ \dfrac{8+4 \sqrt{2} }{ 4-2}} \right]* \left(\dfrac{ \sqrt{2}+2}{2}\right )= \\ \\ \\ \left [ \dfrac{8+4 \sqrt{2} }{ 2}} \right]* \left(\dfrac{ \sqrt{2}+2}{2}\right )=$

$\left [ \dfrac{(8+4 \sqrt{2})*(\sqrt{2}+2) }{ 2*2}} \right]= \\ \\ \\ \left [ \dfrac{8 \sqrt{2}+16+4( \sqrt{2} )^2+8 }{ 4}} \right]= \\ \\ \\ \left [ \dfrac{8 \sqrt{2}+16+8+8 \sqrt{2} }{ 4}} \right]= \left [ \dfrac{16 \sqrt{2}+24 }{ 4}} \right]= \boxed{4 \sqrt{2}+6}$