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Dwandwa Yoga

 

The Dwandwa Yoga or 'duplex combination' can be used for general purpose squaring.

To proceed further we need to know the Dwandwa of certain numbers.

D( a ) = a2

D( ab ) = 2ab

D( abc ) = 2ac + b2

D( abcd ) = 2ad + 2bc

D( abcde ) = 2ae + 2bd + c2

D( abcdef ) = 2af + 2be + 2cd      and so on....

As we can see above, D of any number is the sum of square of the middle number and two times the product of the other pairs.

Square of a number is given by

( ab )2 = D( a ) | D( ab ) | D( b )

( abc )2 = D( a ) | D( ab ) | D(abc) | D( bc ) | D( c )

( abcd )2 = D(a) | D(ab) | D(abc) | D(abcd) | D(bcd) | D(bc) | D (c)


Example : 

(23)2 = (ab)2 = D(a) | D(ab) | D(b)

                    = 4     |    12    |    9

Since Dwanada must have only one digit, we carry over '1' of '12' to LHS.

Therefore it becomes     4 |1 2| 9

Hence the answer is 529


Example 2:

(527)2 = ( abc )2  

           = D( a ) | D( ab ) | D(abc) | D( bc ) | D( c )

           =   25   |     20    |     74   |    28    |   49

           =   25   |2     0    |7     4   |2    8    |4   9

          =   277729


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