*Saamya Samucchaya And
Shoonyam Anyat*

In this section we will solve the quadratic equations based on two sutras
already known to us i.e. * Saamya Samucchaya* (under simple equations) and
* Shoonyam
Anyat* (under simple simultaneous equations).

Consider the following two examples :

1)3+4=6+1x + 3 x + 4 x + 6 x + 1

Using
* Shoonyam Anyat*, we find that the sum of the ratios of the numerators to
the independent factors in each term, on either side are equal. i.e.

3/3 + 4/4 = 6/6 + 1/1

Therefore according to the sutra we have x = 0

Now the above problem can be written as

1 -x+ 1 -x= 1 -x+ 1 -xx + 3 x + 4 x + 6 x + 1 ==>x+x=x+xx + 3 x + 4 x + 6 x + 1By taking x as the common factor from each term (or applying the first meaning of the samucchaye sutra) we get x = 0==>1+1=1+1x + 3 x + 4 x + 6 x + 1 Therefore bySamucchayeformula, we have 2x + 7 = 0 ==> x = -7/2

2)1+1=2+12x + 1 3x + 1 3x + 2 6x + 1 Now1can be written as 1 -2xand so on 2x + 1 2x + 1 Therefore the problem can be rewritten as 1 -2x+ 1 -3x= 1 -3x+ 1 -6x2x + 1 3x + 1 3x + 2 6x + 1 ==>2x+3x=3x+6x2x + 1 3x + 1 3x + 2 6x + 1 Taking x as the common factor we have x = 0 ==>2+3=3+62x + 1 3x + 1 3x + 2 6x + 1By the method discussed in the 'Disguised Problems' under 'Simple Equations' we get6+6=6+66x + 3 6x + 2 6x + 4 6x + 1 Hence we have 12x + 5 = 0 ==> x = -5/12

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