Let x be the greater real root of 225x^2 − 4 = 0 and y be the (unique) real solution of 15y + 2 = 0 (interpreting √225 · y + 2 = 0). Compare x and y.

Introduction / Context: The second relation was typographically unclear. Using Recovery-First Policy, we interpret √225 y + 2 = 0 as (√225)·y + 2 = 0 ⇒ 15y + 2 = 0. We then solve both and compare the numeric values using the greater real root convention for the quadratic.

Given Data / Assumptions:

• 225x^2 − 4 = 0 ⇒ x has two symmetric real roots; take the greater one.
• 15y + 2 = 0 ⇒ single solution y.

Concept / Approach: Solve each: isolate x^2 and y. For comparison, evaluate numerically and select the correct inequality.

Step-by-Step Solution:

Verification / Alternative check: Decimal check: x ≈ 0.133…, y ≈ −0.133…, confirms the inequality.

Why Other Options Are Wrong: They reverse the sign relation or claim equality, which is false given the computed values.

Common Pitfalls: Misreading √225 y as √(225y); the intended linear form is (√225)·y.

Final Answer: If x > y