Generally we come across problems which can be solved by mere observation. But we follow the conventional procedure to get our results. But the hint behind the Sutra enables us to observe the problem completely and find the pattern and finally solve the problem by just observation.

**Example 1 :**

**Solve : x + (1/x) =3/2**

**By usual Conventional method :**

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

x

^{2}+1 5

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

x 2

2 x

^{2 }+ 2 = 5x

2x

^{2}- 5x + 2 = 0

2x

^{2}- 4x - x+2 = 0

2x (x-2) - (x-2) = 0

(x-2) (2x-1) = 0

or x = 2 , (1/2)

**Now by Vilokanam or by mere observation :**

x + 1 5

--- = ----

x 2 can be viewed as ,

x + 1 1

---- = 2 +-----

x 2 where we get our results straight away as x= 2 ,(1/2)

Example 2 :

**x + 5 x + 6 113**

**____ + _____ = ___**

**x + 6 x + 5 56**

**Now by Vilokanam or by mere observation :**

113 49 + 64 7 8

___ = _______ = ___ + ___

56 7 x 8 8 7

x + 5 7 x+5 8

____ = __ or ____ = __

x + 6 8 x+6 7 by splitting the R.H.S and L.H.S on both sides

8x + 40 = 7x + 42 and 7x + 35 = 8x + 48

Solving for x,

x = 42 - 40 = 2 -x = 48 – 35 = 13

x = 2 or x = -13.

**Example 3:**

__Simultaneous Quadratic Equations:__

**Solve: x + y = 9 and xy = 14.**
By mere observation,

xy = 14 gives x = 2, y = 7 or x = 7, y = 2

These two sets satisfy x + y = 9 since 2 + 7 = 9 or 7 + 2 = 9.

Hence the solution.

Similarly,

**Solve : 5x – y = 7 and xy = 6.**
By mere observation,

xy = 6 gives x = 2, y = 3 or x = 3, y = 2

These two sets satisfy 5x - y = 7 since 5(2) -3 = 7 but not 5(3)- 2 = 12.

Hence the solution is x=2 and y =3

Note : You may also like to read finding Cube Roots of any numbers by mere observation.

I was so poor at Maths as a child! Wish I had stumbled upon Vedic Maths earlier.

ReplyDelete@umashankar Sometimes knowing the complex part of maths makes Vedic maths much simpler to learn :):P

ReplyDelete