Resposta:
[tex]\textsf{letra B}[/tex]
Explicação passo a passo:
[tex]\mathsf{\dfrac{(3 + 2\sqrt{2})^{2008}}{(5\sqrt{2} + 7)^{1338}} + (3 - 2\sqrt{2})}[/tex]
[tex]\mathsf{(3 + 2\sqrt{2})^x = (7 + 5\sqrt{2})}[/tex]
[tex]\mathsf{x = log_{(3 + 2\sqrt{2})}\:(7 + 5\sqrt{2})}[/tex]
[tex]\mathsf{x = \dfrac{3}{2}}[/tex]
[tex]\mathsf{\dfrac{(3 + 2\sqrt{2})^{2008}}{[\:(3 + \sqrt{2})^{\frac{3}{2}}\:]^{1338}} + (3 - 2\sqrt{2})}[/tex]
[tex]\mathsf{\dfrac{(3 + 2\sqrt{2})^{2008}}{(3 + \sqrt{2})^{2007}} + (3 - 2\sqrt{2})}[/tex]
[tex]\mathsf{(3 + 2\sqrt{2}) + (3 - 2\sqrt{2}) = \boxed{\mathsf{6}}}\leftarrow\textsf{inteiro par}[/tex]
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Resposta:
[tex]\textsf{letra B}[/tex]
Explicação passo a passo:
[tex]\mathsf{\dfrac{(3 + 2\sqrt{2})^{2008}}{(5\sqrt{2} + 7)^{1338}} + (3 - 2\sqrt{2})}[/tex]
[tex]\mathsf{(3 + 2\sqrt{2})^x = (7 + 5\sqrt{2})}[/tex]
[tex]\mathsf{x = log_{(3 + 2\sqrt{2})}\:(7 + 5\sqrt{2})}[/tex]
[tex]\mathsf{x = \dfrac{3}{2}}[/tex]
[tex]\mathsf{\dfrac{(3 + 2\sqrt{2})^{2008}}{[\:(3 + \sqrt{2})^{\frac{3}{2}}\:]^{1338}} + (3 - 2\sqrt{2})}[/tex]
[tex]\mathsf{\dfrac{(3 + 2\sqrt{2})^{2008}}{(3 + \sqrt{2})^{2007}} + (3 - 2\sqrt{2})}[/tex]
[tex]\mathsf{(3 + 2\sqrt{2}) + (3 - 2\sqrt{2}) = \boxed{\mathsf{6}}}\leftarrow\textsf{inteiro par}[/tex]