Algebraic identity application: Evaluate (2.247)^3 + (1.730)^3 + (1.023)^3 - 3 * 2.247 * 1.730 * 1.023, divided by [(2.247)^2 + (1.730)^2 + (1.023)^2 - 2.247*1.730 - 1.730*1.023 - 2.247*1.023].

Introduction / Context:
This problem directly uses a well-known algebraic identity. When x + y + z ≠ 0, the expression (x^3 + y^3 + z^3 - 3xyz) / (x^2 + y^2 + z^2 - xy - yz - zx) simplifies elegantly to x + y + z.

Given Data / Assumptions:

• x = 2.247, y = 1.730, z = 1.023
• We assume standard algebraic identities apply and no rounding is needed before substitution.

Concept / Approach:
Use the identity: (x^3 + y^3 + z^3 - 3xyz) / (x^2 + y^2 + z^2 - xy - yz - zx) = x + y + z, provided x + y + z ≠ 0. Here, the numbers are chosen so their sum is exact and simple.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 1.730, 4, 5.247: These are distractors derived from partial sums or misapplied identities. Only the exact sum 5 satisfies the identity here.

Common Pitfalls:

• Attempting to expand everything numerically, increasing chances of arithmetic error.
• Forgetting the identity or misremembering coefficients.

Final Answer: