What is the result of \(\dfrac{0.5^3 + 0.1^3 - 0.6^3}{3 \times 0.5 \times 0.1 \times 0.6}\)?
-1
Step 1 – use the identity:
If \(a + b + c = 0\), then \(a^3 + b^3 + c^3 = 3abc\).
Step 2 – choose \(a, b, c\):
Take \(a = 0.5,\ b = 0.1,\ c = -0.6\). Then \(a + b + c = 0.5 + 0.1 - 0.6 = 0\) ✓.
Step 3 – rewrite the numerator:
\(0.5^3 + 0.1^3 - 0.6^3 = 0.5^3 + 0.1^3 + (-0.6)^3 = 3 \times 0.5 \times 0.1 \times (-0.6)\)
Step 4 – form the ratio:
\(\dfrac{3 \times 0.5 \times 0.1 \times (-0.6)}{3 \times 0.5 \times 0.1 \times 0.6} = \dfrac{-0.6}{0.6} = -1\)
Hence the result is −1.
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