Question

Qual o valor de√43 + √31 + √21 + √13 + √7 + √3 + √1 :

a) ( ) -7 b) ( ) 5 c) ( ) 6 d) ( ) 7​

Answer 1

Qual o valor de$\ \ \ \sqrt{43+ \sqrt{31 + \sqrt{21+ \sqrt{13+ \sqrt{7+\sqrt{3+\sqrt{1}}}}}}}$:

  a) -7

  b) 5

   c) 6

x  d) 7​

$\ \ \ \sqrt{43+ \sqrt{31 + \sqrt{21+ \sqrt{13+ \sqrt{7+\sqrt{3+\sqrt{1}}}}}}}\\= \sqrt{43+ \sqrt{31 + \sqrt{21+ \sqrt{13+ \sqrt{7+\sqrt{3+1}}}}}}\\= \sqrt{43+ \sqrt{31 + \sqrt{21+ \sqrt{13+ \sqrt{7+\sqrt{4}}}}}}\\= \sqrt{43+ \sqrt{31 + \sqrt{21+ \sqrt{13+ \sqrt{7+2}}}}}\\\\= \sqrt{43+ \sqrt{31 + \sqrt{21+ \sqrt{13+ \sqrt{9}}}}}\\= \sqrt{43+ \sqrt{31 + \sqrt{21+ \sqrt{13+ 3}}}}\\= \sqrt{43+ \sqrt{31 + \sqrt{21+ \sqrt{16}}}}\\= \sqrt{43+ \sqrt{31 + \sqrt{21+ 4}}}\\= \sqrt{43+ \sqrt{31 + \sqrt{25}$

$= \sqrt{43+ \sqrt{31 + 5}}\\= \sqrt{43+ \sqrt{36}}\\= \sqrt{43+ 6}\\= \sqrt{49}\\=7$