When the samuccaya is the same, that samuccaya is zero

The word samuccaya has various meanings in different applications and is useful in solving equations visually.

Example 1:

Simple Equations ( Type 1):

6x+2x = 3x +7x

Here 'x' is same on both sides and so 'x' is Zero

Simple Equations ( Type 2):

(x+1)(x+2)=(x+5)(x+4)

Here 'x' is same on both sides and so 'x' is Zero

Example 2:

Simple Fractions (Type 1):

1 /(3x-1) + 1/(6x-1)

Here,the numerator is same ,i.e=1 and so we set the denominator to zero

3x-1+6x-1 =0

x= 1/9

Simple Fractions (Type 2):

3x+9(N1) 5x+7(N2)

--------- = ----------

5x+7(D2) 3x+9(D2)

Here ,the sum of the numerators and the sum of denominators are the same and so their sum is equal to zero

i.e; N1+N2=D1+D2 =0

3x+9+5x+7 =0 ,so x = 2

Example 3:

Quadratic Equations :

 1         1        1         1

---   + ---   = ---   + ---

X-4    X-8     X-3    X-9

Here,the Numerators N is same and sum of the denominators are equal.

So, D1+D2 =D3+D4 =0

2x-12 =0 , giving x = 6

Example 4:

Cubic Equations (Type 1)

(x-4)³ + (x-8)³ = 2(x-6)³

Here,the powers are same on both sides ,x is same and also numerical value is equal on both sides ,so the equations are equated to zero

x-4+x-8 =2(x-6) =0

Therefore x= 6

Cubic Equations (Type 2)

(x+2)³         x+3

-------- = -----

(x+6)³       x+5

Here ,N1+D1 =N2+D2 and so they are equated to zero

2x+8=0 giving x  = - 4

The above vedic sutra will be quite helpful in Competitive exams when we know the techniques involved.

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