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# Vedic Math Sutra: Sutra-9 Chalana-Kalanabhyam

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Chalana-Kalanabhyam” is a Sanskrit phrase used in Vedic Mathematics. The term translates to “by movement and by position.” It’s one of the sixteen Sutras, or word formulae, proposed by Sri Bharati Krishna Tirthaji in his book “Vedic Mathematics,” each of which he claimed represented a mathematical principle.

The Chalana-Kalanabhyam Sutra mainly applies to simplify specific algebraic equations, especially quadratic and cubic ones.

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

Let’s take an example of how to apply the Chalana-Kalanabhyam Sutra for solving cubic equations.

#### Consider the cubic equation

x^3 – 6x^2 + 11x – 6 = 0

#### This equation can be solved using Chalana-Kalanabhyam as follows:

1. First, note the coefficients of the equation: 1 (for x^3), -6 (for x^2), 11 (for x), and -6 (the constant).
2. Start by assuming the root of the equation to be ‘x.’ Consider ‘x’ and start by subtracting the coefficient x^2 from it, that is, x – (-6) = x + 6.
3. Now, multiply this root with the coefficient of x (11) and subtract the constant term (-6). This gives (x + 6)*11 – 6.
4. If the result of this operation is zero, then we have found the root of the cubic equation. However, in this case, you will find that for x = 1, the result is indeed zero, making x = 1 a root of this cubic equation.
5. The remaining roots can be found by dividing the original cubic equation by (x – 1), resulting in a quadratic equation that can be solved using standard methods.

This example illustrates the use of Chalana-Kalanabhyam for solving cubic equations. However, remember that the applicability of this sutra is limited and does not extend to all types of equations.

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