Question

(CN) Sejam P= (1+1/5)(1+1/5)(1+1/7)(1+1/7)(1+1/9)(1+1/11) e Q= (1-1/15)(1-1/7)(1-1/9)(1-1/11), Qual e o valer de (Raiz quadrada de P/Q?)
Com calculos pfv

Answer 1

Vamos resolver primeiramente o "P":

$\mathsf{P=(1+ \frac{1}{3})(1+ \frac{1}{5})(1+ \frac{1}{7})(1+ \frac{1}{9})(1+ \frac{1}{11})} \\ \\ \mathsf{P=( \frac{4}{3})( \frac{6}{\not5})( \frac{8}{7} )( \frac{\not 10}{\not 9})( \frac{\not12}{11} )} \\ \\ \mathsf{P= \frac{4}{3}* \frac{6}{1}* \frac{8}{7} * \frac{2}{3}* \frac{4}{11}} \\ \\ \mathsf{P= \frac{1536}{693} }$

Agora o Q:

$\mathsf{Q=( 1-\frac{1}{5})(1- \frac{1}{7})(1- \frac{1}{9})(1- \frac{1}{11})} \\ \\ \mathsf{Q=( \frac{4}{5})( \frac{\not6}{7})( \frac{8}{\not9})( \frac{10}{11})} \\ \\ \mathsf{Q= \frac{4}{5}* \frac{2}{7}* \frac{8}{3} * \frac{10}{11}} \\ \\ \mathsf{Q= \frac{640}{1155} }$

$\mathsf{ \sqrt{ \frac{P}{Q}}= \sqrt{ \frac{ \frac{1536}{693}} { \frac{640}{1155} } } = \sqrt { \frac{1536}{693} * \frac{1155}{640} } = \sqrt{ \frac{1774080}{443520} }= \sqrt{4}=\boxed{\mathsf{2}}}$

Answer 2

Resposta:

2

Explicação passo-a-passo: