Question

<br />$\frac{4}{ \sqrt{5 + 1 \sqrt[4]{5 + 1 \sqrt[8]{5 + 1 \sqrt[16]{5 + 1} } } } }$<br />​

Answer 1

Resposta:

Vamos lá!

$\dfrac{4}{\sqrt{5+1\sqrt[4]{5+1\sqrt[8]{5+1\sqrt[16]{5+1} } } } } =\\\\\\\dfrac{4}{\sqrt{5+1\sqrt[4]{5+1\sqrt[8]{5+1 [6^{\frac{1}{16}} ] } } } } =\\\\\\\dfrac{4}{\sqrt{5+1\sqrt[4]{5+1[6^{\frac{1}{8} } .6^{\frac{1}{16}} ] } } } } =\\\\\\\dfrac{4}{\sqrt{5+1[{6^{\frac{1}{4} }.6^{\frac{1}{8} } .6^{\frac{1}{16}} ] } } } } =\\\\\\\dfrac{4}{{6^{\frac{1}{2} }.{6^{\frac{1}{4} }.6^{\frac{1}{8} } .6^{\frac{1}{16}} } } } } =\\\\\\\dfrac{4}{{6^{\frac{8+4+2+1}{16} }} } }=\dfrac{4}{{6^{\frac{15}{16} } } }=$

$\dfrac{4}{{\sqrt[16-14]{6^{15-14 } } } }=\dfrac{4}{{\sqrt[2]{6^{1 } } } }=\\\\\\\dfrac{4}{{\sqrt[]{6 } } }*\sqrt{6} =\dfrac{4\sqrt{6} }{{\sqrt[]{36} } } }=\\\\\\\dfrac{4\sqrt{6} }{{{6} } } }=\dfrac{2\sqrt{6} }{3}$