Question

Cho T=√20+√20+...+√20+³√24+³√24+...+³√24

                                   (2006 dấu căn)                                  (2006 dấu căn)

CM: 7<T<8

 

Answer 1

<br class="Apple-interchange-newline"><div id="inner-editor"></div>T=√20+√20+...+√20+3√24+3√24+...+3√24>√20+3√24>7(1)Mặt khác:

√20+√20+...+√20<√20+√20+...+√20+√25=5

 Và:

 

Answer 2

 

 

<br class="Apple-interchange-newline"><div id="inner-editor"></div>T=√20+√20+...+√20+3√24+3√24+...+3√24>√20+3√24>7(1)Mặt khác:

 

 

√20+√20+...+√20<√20+√20+...+√20+√25=5

Và:

 

<br class="Apple-interchange-newline"><div id="inner-editor"></div>3√24+3√24+...+3√24<3√24+3√24+...+3√24+3√27=3

 

 Nên T=√20+√20+...+√20+3√24+3√24+...+3√24<8(2).Từ (1) và (2), ta có:   

Answer 3

\(11224hu\)