Vedic Maths : Ekadhikena Purvena

Vedic Maths : Ekadhikena Purvena

Ekadhikena Purvena

one added to the previous digit

एकाधिकेना पूर्वेण

Now let's assume

A = xp + a

B = xp + b

A * B = px ( px + a + b) + ab

Here is one special case. Assume

x = a + b

px ( px + a + b) + ab

= px ( px + x ) + ab

= (x ^ 2) (p) ( p + 1) + ab

We know, 5 + 5 = 10

Let's take x = 10 , p = 1

Then, here is a special case of making square for any digit ending with 5.

A = xp + a	B = xp + b	a	b	n	p	( x ^ 2 ) ( p ) ( p + 1 )	ab
15	15	5	5	1	1	100 * 1 * 2 = 200	25
25	25	5	5	1	2	100 * 2 * 3 = 600	25
35	35	5	5	1	3	100 * 3 * 4 = 1200	25
45	45	5	5	1	4	100 * 4 * 5 = 2000	25
55	55	5	5	1	5	100 * 5 * 6 = 3000	25
65	65	5	5	1	6	100 * 6 * 7 = 4200	25
75	75	5	5	1	7	100 * 7 * 8 = 5600	25
85	85	5	5	1	8	100 * 8 * 9 = 7200	25
95	95	5	5	1	9	100 * 9 * 10 = 9000	25
105	105	5	5	1	10	100 * 10 * 11 = 11000	25
115	115	5	5	1	11	100 * 11 * 12 = 13200	25
125	125	5	5	1	12	100 * 12 * 13 = 15600	25
155	155	5	5	1	15	100 * 15 * 16 = 24000	25
185	185	5	5	1	18	100 * 18 * 19 = 34200	25

Here are few more examples

A = xp + a	B = xp + b	a	b	n	p	( x ^ 2 ) ( p ) ( p + 1 )	ab
37	33	7	3	1	3	100 * 3 * 4 = 1200	21
79	71	9	1	1	7	100 * 7 * 8 = 5600	9
87	83	7	3	1	8	100 * 8 * 9 = 7200	21
96	94	6	4	1	9	100 * 9 * 10 = 9000	24
97	93	7	3	1	9	100 * 9 * 10 = 9000	21
98	92	8	2	1	9	100 * 9 * 10 = 9000	16
99	91	9	1	1	9	100 * 9 * 10 = 9000	9
114	116	4	6	1	11	100 * 11 * 12 = 13200	24
191	109	91	9	2	1	10000 * 1 * 2 = 20000	819
793	707	93	7	2	7	10000 * 7 * 8 = 560000	651
884	816	84	16	2	8	10000 * 8 * 9 = 720000	344

0 comments:

Post a Comment