Śūnyaṃ Sāmyasamuccaye — When the sum is the same, that sum is zero

शून्यं साम्यसमुच्चये — Shunyam Saamyasamuccaye

When the sum is the same, that sum is zero. If the same expression appears on both sides of an equation with equal sums, it equals zero — the equation solves instantly.

Why it works: If f(x) = g(x) and both sides have the form where a common factor x+k appears in the sum of terms, then x+k=0 is a root. This catches algebraic structure that makes one term vanish.

Speed advantage: Pattern recognition reduces 6-step algebraic manipulation to 1.

Best for

• Solving certain classes of algebraic equations instantly

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Originally published at https://www.sutraflow.app/sutras/shunyam-saamyasamuccaye