Sixth Meaning of Samucchaya

Applying the meaning of Samucchaya  as 'total' in a different application, we find the solution of what many books refer to as 'Harder equations' to be very simple.

Consider the following example

              1     +     1      =      1     +     1    
            x + 2     x - 9        x - 3      x - 4

The Vedic sutra says that, if other elements being equal, the sum total of the denominators on LHS and the  total on RHS be same, then the total is equated to zero.

i.e.   if  D₁ + D₂ = D₃ + D₄   then  D₁ + D₂ = 0 is the solution.

   Here        D₁ + D₂ = 2x -7

                  D₃ + D₄ = 2x -7

Hence as per the sutra we have 2x - 7 = 0

                        ==> x = 7/2

Example 2 :

              1      +      1      =       1      +     1   
            x + 4       x + 5         x + 1      x + 8

We find that D₁ + D₂ = D₃ + D₄    = 2x + 9

Hence according to the sutra 2x + 9 = 0

                                ==> x = -9/2

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