Find-the-cube-of-the-number-N-7-3-7-3-7-3-7-3-

Question Number 137585 by bramlexs22 last updated on 04/Apr/21

F i n d t h e c u b e o f t h e n u m b e r

N = \sqrt{7 \sqrt{3 \sqrt{7 \sqrt{3 \sqrt{7 \sqrt{3 \sqrt{7 \sqrt{3 \dots}}}}}}}}

Answered by bemath last updated on 04/Apr/21

N = 7^{\frac{1}{2} + \frac{1}{8} + \frac{1}{32} + \frac{1}{128} + \dots} . 3^{\frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \dots}

N = 7^{\frac{1 / 2}{1 - 1 / 4}} . 3^{\frac{1 / 4}{1 - 1 / 4}}

N = 7^{\frac{2}{3}} . 3^{\frac{1}{3}} \Leftrightarrow N^{3} = 49 \times 3

N^{3} = 147

Answered by mr W last updated on 04/Apr/21

N = \sqrt{7 \sqrt{3 N}}

N^{2} = 7 \sqrt{3 N}

N^{4} = 7^{2} \times 3 N

\Rightarrow N^{3} = 7^{2} \times 3 = 147

Facebook Tweet Pin