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# Vedic Math Sutra: Sutra 8 -Puranapuranabhyam

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The Vedic Math Sutra 8 is called Puranapuranabhyam, which translates to – By the completion or non-completion. This sutra helps perform calculations involving complements or non-complements of numbers. Let’s explore how this sutra can be applied.

Recommended Reading: VEDIC MATH SUTRA: SUTRA 3 – URDHAVA – TIRYAGBYHAM

This sutra can be used to factorize and solve quadratic and cubic & bi-quadratic equations.

#### The Sutra States

“Puranapuranabhyam” (By the completion or non-completion) – “Whatever is to be added to the completed (Purana) or non-completed (Apurna) in one is added to the other.”

To understand this sutra better, let’s consider an example.

#### Example 1

Solve the quadratic equation 2x^2 + 5x – 3 = 0 using Vedic Mathematics.

Step 1: Understand the Quadratic Equation

The given quadratic equation is 2x^2 + 5x – 3 = 0.

Step 2: Identify the Values

From the equation, we can identify the values as follows:

a = 2

b = 5

c = -3

Step 3: Apply the Puranapuranabhyam Sutra

The product of the sum and difference of two numbers is equal to the difference of their squares.

Let’s find two numbers whose product equals ac, which is 2*(-3) = -6, and whose sum is equal to b, which is 5.

Let’s say m and n are those two numbers.

Step 4: Factorize the Quadratic Equation

We need to find two numbers whose product is -6 and whose sum is 5.

By inspection, we can see that 6 and -1 fit these conditions since 6 * (-1) = -6 and 6 + (-1) = 5.

Therefore, we can rewrite the quadratic equation as follows:

2x^2 + 6x – x – 3 = 0

Now, we can factorize it by grouping

2x(x + 3) – 1(x + 3) = 0

Notice that we have a common factor of (x + 3). Factoring it out, we get:

(x + 3)(2x – 1) = 0

Step 5: Solve for x

Now, we’ll set each factor equal to zero and solve for x:

x + 3 = 0 –> x = -3

2x – 1 = 0 –> 2x = 1 –> x = ½

These are the two roots of the quadratic equation 2x^2 + 5x – 3 = 0, obtained using Vedic Mathematics.

Therefore, the roots are x = -3 and x = 1/2.

You can verify these roots by substituting them back into the original equation.

The Puranapuranabhyam sutra can be a helpful tool in performing calculations more efficiently by utilizing complements and non-complements. However, practicing and familiarizing yourself with various applications of Vedic Math sutras is essential to use them effectively.

Recommended Reading: HOW VEDIC MATH CAN HELP GEN Z TO OVERCOME MATH FEAR

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