Algebric Proof for Ekdhikena prvena — Vedic Mathematics

Posted: September 16, 2012 in Mathematics
Tags: , , , , , , , ,

The first and easiest sutra in vedic mathematics is Ekdhikena prvena which means “By one more than the previous one”.

We are well aware of this of this sutra. It is applied for square of numbers ending in 5.

General Format : a5 * a5 = (a)*(a+1) /25

For example : 65 * 65 = (6) * (6+1)/25 = (6)*(7)/25 = 42/25

hence 65 * 65 = 4225

Now, its time to know how the sutra came! The proof is very easy !

(a+b)^ 2 = a^2 + b^2 + 2ab

(ax+b)^2 = a^2 x^2 + b^2 + 2abx

we can write 65 ^ 2 as (10*6 + 5)^2

Hence x will always be 10 and b will always be 5. a will vary.

General form is : (10a + 5) ^ 2 where a=1,2….

(10a + 5) ^ 2 = a^2 10^2 + 2 (10a) (5) + 5^2
= a^2 10^2 + 10^2 a + 5^2
= (a^2 + a).10^2 +d^2
= a(a + 1).10^2 + 25

Clearly 10a + 5 represents two-digit numbers 15, 25, 35, ——-,95 for the
values a = 1, 2, 3, ——-,9 respectively. In such a case the number (10a + 5)^2 is
of the form whose L.H.S is a (a + 1) and R.H.S is 25, that is, a (a + 1) / 25.

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