Sūtra 5 of 16

Śūnyaṁ Sāmyasamuccaye

When the sum is the same, that sum is zero

Solving equations where a particular sum equals zero.

When to use

Equations like (x+a)/(x+b) = (x+c)/(x+d) where a+d = b+c.

How it works

If both sides of an equation, after simplification, share a common 'sameness' (like equal sums of numerators and denominators), that sameness equals zero, giving an instant root.

Memory formula

If the same sum appears on both sides, set that common sum to zero.

Worked examples

Problem 1

(x+2)/(x+3) = (x+4)/(x+5)

0/3

Modern applications

Where this ancient technique still lives in today's world.

AI / ML

Equation simplification

Symbolic solvers (SymPy, Mathematica) detect 'when the sum is the same, that sum is zero' as a fast-path simplification.

Code in your favourite language

If both sides share a common sum, that sum equals zero.

Python

# 12x + 7 = 7x + 7  ->  common 7  ->  x = 0
def solve_common_sum(a, b, c, d):
    if b == d:
        return 0  # the variable factor itself is zero
    return None

print(solve_common_sum(12, 7, 7, 7))

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