Chứng minh: 1/44 +1/61 +1/85 < 1/6

2 bình luận về “Chứng minh: 1/44 +1/61 +1/85 < 1/6”

1. quy đồng $\dfrac{1}{44}$+$\dfrac{1}{61}$+$\dfrac{1}{85}$ ; $\dfrac{1}{6}$

     $\dfrac{1}{44}$=$\dfrac{1x61x85x6}{44x61x85x6}$=$\dfrac{3110}{1288849}$

     $\dfrac{1}{61}$=$\dfrac{1x44x85x6}{61x44x85x6}$=$\dfrac{3740}{1288849}$

   $\dfrac{1}{85}$=$\dfrac{1x44x61x6}{85x44x61x6}$=$\dfrac{16044}{1288849}$

   $\dfrac{1}{6}$=$\dfrac{1x44x61x85}{6x44x61x85}$=$\dfrac{225590}{1288849}$

    ta có

     $\dfrac{3110}{1288840}$+$\dfrac{3740}{1288849}$+$\dfrac{16044}{1288849}$=$\dfrac{22894}{1288849}$

           $\dfrac{22894}{1288849}$<$\dfrac{225590}{1288849}$( vì 22894<225590 )

                          vậy $\dfrac{1}{44}$+$\dfrac{1}{61}$+$\dfrac{1}{85}$<$\dfrac{1}{6}$

    

   Trả lời
2. Giải

   1/6 = 3/18

   Ta có :

   18 \vdots 1;2;3;6;9;18

   Mà 3 = 1+1+1

   => 3/18 = 1/18 + 1/18 + 1/18

   => 1/6 = 1/18 + 1/18 + 1/18

   Ta thấy :

   1/44 < 1/18

   1/61 < 1/18

   1/85 < 1/18

   => 1/44 + 1/61 + 1/85 < 1/18 + 1/18 + 1/18

   => 1/44 + 1/61 + 1/85 < 1/6 ( điều phải chứng minh )

    

   Trả lời