Question

13 [x] + 25 {x} = 271 then x=
(where {x} is fractional part and [oc] u
integral part of x)​

Answer 1

Given :  

13 [x] + 25 {x} = 271  

To Find :  x  

Solution:

Minimum value of   {x}  = 0

Maximum value of   {x}  < 1

0  ≤  25 {x}  < 25

13 [x]  ≤ 13 [x] +  25 {x}  <  13 [x] +  25

13 [x] + 25 {x} = 271  

13 [x]  ≤   271    <  13 [x]  + 25

13 [x]  ≤   271

=>  x  <  21    

271    <  13 [x]  + 25

=> 13 [x] >  246

=>   x >  19

19  <  x   < 21

case 1  :  19 < x < 20

=> 13(19)  +   25 {x} = 271

=>  25 {x} = 24

=> {x} = 24/25  =  0.96

x = 19.96

case 2  :  20 < x < 21

=> 13(20) +   25 {x} = 271

=>  25 {x} = 11

=>  {x} = 11/25  =  0.44

x = 20.44

x = 19.96  , 20.44

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