Recognize a perfect-square structure: Evaluate (3.65^2 + 2.35^2 − 2 × 2.35 × 3.65) / 1.69 by converting the numerator into a binomial square.

Introduction / Context:
This is a direct application of the identity x^2 + y^2 − 2xy = (x − y)^2. Spotting this pattern allows you to reduce the problem to a simple square and then divide by a given constant. It is a staple technique in simplifying quadratic-looking expressions quickly.

Given Data / Assumptions:

• Numerator: 3.65^2 + 2.35^2 − 2 × 3.65 × 2.35.
• Denominator: 1.69.

Concept / Approach:
Apply (x − y)^2 when you see x^2 + y^2 − 2xy. Here x = 3.65 and y = 2.35, so x − y = 1.30. Hence the numerator is simply 1.30^2. Then divide by 1.69 to finish. The numbers are intentionally chosen so that the final ratio is exact.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 1.69: That is the numerator before division, not the final value.
• 2.35 and 3.65: Misread constants or skipped squaring/identity step.

Common Pitfalls:

• Changing the sign in −2xy and producing (x + y)^2 instead.
• Rounding 1.3^2 incorrectly; it is exactly 1.69.

Final Answer: