Question

Questão 13 da UFF. ME AJUDEM PFV!!

Answer 1

Resposta:

Alternativa c)

Explicação passo-a-passo:

$\displaystyle \sqrt[3]{x^{log_{3}\sqrt[3]{x}}} =3\\\\x^{log_{3}\sqrt[3]{x}}=3^{3}\\\\x^{log_{3}x^{\frac{1}{3}}}=3^{3}\\\\x^{\frac{1}{3}.log_{3}x}=3^{3}\\\\log_{3}(x^{\frac{1}{3}.log_{3}x})=log_{3}(3^{3})\\\\\frac{1}{3}.log_{3}x}.log_{3}x=3log_{3}3\\\\(log_{3}x)^{2}=9\\\\log_{3}x=\pm\sqrt{9} =\pm3\\\\\\log_{3}x=3 \Rightarrow3^{3}=x \Rightarrow x=27\\Ou\\log_{3}x=-3 \Rightarrow3^{-3}=x \Rightarrow x=\frac{1}{27} \\\\\\S=\{27,\frac{1}{27}\}$

O produto das raízes (p)

$\displaystyle p=27.\frac{1}{27}=1$