VEDIC MATHS-96

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VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 96 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Quadratic Equations-III"

Reference:

We had already learn about "Quadratic Equations-I" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-94".

We had already learn about "Quadratic Equations-II" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-95".

Special Case of Quadratic Equations—Reciprocals:
Case C

1. Here we have our first sum: x - 1/x = 5/6.

Here again we have to be careful, because there is a minus sign. So we find the factors of 6, which are 1, 2, 3 and 6. We can’t use 1 and 6, because they don’t give us ; so we take 2 and 3 as reciprocals. Since 3/2 is greater than 2/3, we put that first and we have the right-hand side as . So here we’ll 3/2 - 2/3.

Note that the symbol is minus. 
So here we’ll split the right-hand side like this: 
 x - 1/x = 5/6 = 3/2 - 2/3.
The minus sign is important here. So we’ll get x = 3/2 or -2/3.

Answer:
x = 3/2 or x = -2/3.

2. Here we have our first sum: x - 1/x = 45/14.

Here again we find the factors of 14, which are 1, 2, 7 and 14. We can’t take 1 and 14, because they won’t give us 45/14 , so instead, we go for 2 and 7 as reciprocals.
Since 7/2 is greater than 2/7, we put that first and we have the right-hand side as we get is x = 7/2 - 2/7.
So now our sum looks like this:
x - 1/x = 45/14 = 7/2 - 2/7.
The minus sign is important here. So we’ll get x = 7/2 or -2/7.

Answer:
x = 7/2 or x = -2/7.

3.  x/(x+3) + (x+3)/x = 15/56.

Here the factors of 56 are 1, 2, 4, 8, 7, 28 and 14. Out of these, we take 7 and 8, because their reciprocals give us . So we have the right-hand side as 8/7 - 7/8
Following the same pattern as in the previous sums, we’ll solve like this:
x/(x+3) + (x+3)/x = 15/56 = 8/7 - 7/8.
x/(x+3) = 8/7
       7x = 8x + 24
7x - 8x = 24
       - x = 24
         x = -24
or
x/(x+3) = 7/8
       8x = 7x + 21
 8x -7x = 21
         x = 21
         x = 21
Answer:
x = -24 & x = 21.

4. (5x+9)/(5x-9) + (5x-9)/(5x+9) = 56/45.

Here the factors of 45 are 1, 3, 5, 9 and 15. We use 9 and 5, because their reciprocals subtracted give us 56/45.
Here we’ll split the right-hand side into two reciprocals. So what we get is :
(5x+9)/(5x-9) + (5x-9)/(5x+9) = 56/45 = 9/5 - 5/9.
We’ll now solve to find the two values of x:
(5x+9)/(5x-9) = 9/5
        25x - 45 = 45x - 81
             - 20x = -81 -45
                   x = -126/-20
                   x =  63/10
or
(5x+9)/(5x-9) = 9/5
       45x + 81 = -25x - 45
               70x = 45 -81 
                   x = 36/-70
                   x = -18/35
Answer:
x =  63/10 & x = -18/35

The simplicity of this method can be vouched from examples given above.

You may try following examples.
1. x - 1/x = 9/20.
2. x/(x+1) - (x+1)/x = 7/12.
3. (x+1)/(x+2) - (x+2)/(x+1) = 56/45.

In next blog we will discuss about "Raising to Fourth and Higher Powers-I".     

Are you excited for this?...
Then, please wait for it.
I will post my new blog in next week.

We will meet very soon through our next  blog. Till that stay connected, stay healthy and stay safe.

Thanks

for giving your valuable time.

Good day😊

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