If a = 0.02, b = 0.03, c = –0.05, and a + b + c = 0, find (a³ + b³ + c³) ÷ (3abc)

Question

If a = 0.02, b = 0.03, c = –0.05, and a + b + c = 0, find (a³ + b³ + c³) ÷ (3abc)

1. A. –1
2. B. 0
3. C. 1 (Correct answer)
4. D. 2

Correct Answer

Option C — 1

Detailed Solution & Explanation

The correct answer is 1.

Key Points

• When a + b + c = 0, the identity a³ + b³ + c³ = 3abc holds.
• The question confirms 0.02 + 0.03 − 0.05 = 0, so the condition is met.
• Therefore (a³ + b³ + c³) ÷ (3abc) = 3abc ÷ 3abc = 1 — no need to cube the decimals at all.
• Spotting that the three terms sum to zero turns an ugly decimal computation into a one-step identity; always check that sum first.