Use an identity to simplify a ratio of sums of squares: Evaluate [(3.537 − 0.948)^2 + (3.537 + 0.948)^2] / [(3.537)^2 + (0.948)^2].

Introduction / Context:This expression is designed for application of a standard algebraic identity. Recognizing structure avoids arduous arithmetic with decimals.

Given Data / Assumptions:

• a = 3.537, b = 0.948.
• Expression: [(a − b)^2 + (a + b)^2] / (a^2 + b^2).

Concept / Approach:Identity: (a − b)^2 + (a + b)^2 = 2a^2 + 2b^2 = 2(a^2 + b^2). Substitute this into the expression to simplify immediately.

Step-by-Step Solution:

Verification / Alternative check:Compute a^2 + b^2 numerically if desired; the factor of 2 cancels regardless of specific values, confirming the identity-based simplification.

Why Other Options Are Wrong:4 and 4.485 overstate the result; 2.589 is arbitrary. 1 would occur if the numerator equaled the denominator, which is not the case here.

Common Pitfalls:Expanding each square separately and then adding may invite arithmetic errors. Spot the identity first to save time.

Final Answer:2