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Reciprocals

 

This part deals with reciprocals. Using the method explained below many such problems can be solved merely by mental calculation alone.

Let us consider


           x +  1  =  10
                 x       3
 

Under the usual method, we cross multiply to obtain a quadratic equation which is then solved to obtain 'x'.

But by Vilokanam  sutra of Vedic mathematics, the problem can be solved merely at a glance by simple mental calculation.


   10/3 can be written as  3 +  1/3
   
   Therefore    x  +   1   =   3  +   1 
                              x                3                   
 

                                       ==>    x  =  3   or   1/3


Similarly,


2)    x  +   1   =   37   =   6  +  1 
                x        6               6 
  
       Therefore from the sutra we have x = 6 or 1/6                    
         
3)    1    +  x + 1    =  26   =   5  +  1 
     x + 1      1            5                5

      Therefore from the sutra we have  x + 1 = 5  or  1/5
                   ==>  x = 4   or  -4/5

4)    x - 3  +  x + 3   =   5   =  2  +  1 
       x + 3     x - 3        2              2

      Therefore  we have   x - 3   =   2  or   1
                                     x + 3                 2
           ==>  x = -9 or 9
           
5)   x  +  1   =   13 
              x        6
     Here 13/6 can be split up into  2/3 + 3/2
     
     Therefore   x  +  1  =  2  +  3
                               x     3     2
       ==>   x = 2/3  or  3/2
       
6)     x    +  x + 1   =  25  =  3  +  4
      x + 1       x          12      4     3
     
     ==>    x    =  4   or   3
           x + 1      3        4
          
     ==>   x  =  -4  or  3
     
7)    x  -   1  =   5   =   3  -  2
               x       6       2     3
             
       Therefore  x = 3/2  or  -2/3
       
8)    x    -  x + 2  =  15  =  8  -  7
     x + 2       x        56     7     8
    
    ==>   x    =  8  or  -7
         x + 2     7        2
        
    ==>   x = -16  or  -14/9       
 

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