If a + b + c = 0 (with a, b, c non-zero), what is the value of \(\frac{a^3 + b^3 + c^3}{abc}\)?

A. 1

B. 3

C. 9

D. 0

Doubtly AI Asked 27 Oct 2026 AI-generated · not yet verified ssc cgl Save WhatsApp Report

1 answer

Best answer

Answer: B. 3

Answer: (B) 3

Identity: \(a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)\).

When a + b + c = 0, \(a^3 + b^3 + c^3 = 3abc\), so the ratio is 3. (Example: 1, 2, −3 gives 1 + 8 − 27 = −18 and abc = −6.)

Doubtly AI · 27 Oct 2026 AI-generated · not yet verified Report

Was this answer helpful?