Vedic Maths : yavadunam tavadunikrtya varganca yojayet


yavadunam tavadunikrtya varganca yojayet

what ever the deficiency subtract that deficit from the number and write along side the square of that deficit

यावदूनम् तावदूनीकृत्य वर्ग च योजयेत्

We already know

A = x + a
B = x + b

A * B = (x + a) * (x + b)
= x ^ 2 + x ( a + b ) + ab
= x ( x + a + b) + ab

Here, let's take a special case of finding square. A = B , so a = b 

A * B = A * A 

x ( x + a + a) + a*a = x ( x + 2a) + a ^ 2 

= x [ (x + a) + a] + a ^2 

But as we know x + a = A

So, x [ (x + a) + a] + a ^ 2 = x ( A + a ) + a ^ 2

Here, 'a' can be negative also

For example 

A = x + a

x

a

n

x *  [ A + a )

a ^ 2

A ^ 2

9

10

-1

1

10 * ( 9 - 1 ) =  80

1

81

8

10

-2

1

10 * ( 8 - 2 ) =  60

4

64

11

10

+1

1

10 * ( 11 + 1 ) =  120

1

121

12

10

+2

1

10 * ( 12 + 2 ) =  140

4

144

13

10

+3

1

10 * ( 13 + 3 ) =  160

9

169

14

10

+4

1

10 * ( 14 + 4 ) =  180

16

196

15

10

+5

1

10 * ( 15 + 5 ) =  200

25

225

19

10

+9

1

10 * ( 19 + 9 ) =  280

81

361

91

100

-9

2

100 * ( 91 - 9 ) =  8200

81

8281

94

100

-6

2

100 * ( 94 – 6 ) = 8800

36

8836

97

100

-3

2

100 * ( 97 – 3 ) = 9400

9

9409

108

100

+8

2

100 * (108 + 8 ) = 11600

64

11664

989

1000

-11

3

1000 * ( 989 – 11) = 978000

121

978121

9989

10000

-11

4

10000 * ( 9989 – 11 ) = 99780000

121

99780121

 

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