Let x be the greater real root of x^2 − 32 = 112 and y satisfy y − √169 = 0. Compare x and y.

Introduction / Context: One equation is a shifted square giving an exact integer root; the other is a simple radical linear relation. We compute both values and compare using the greater-root convention where applicable.

Given Data / Assumptions:

• x^2 − 32 = 112 ⇒ x^2 = 144 ⇒ roots ±12; greater x = 12.
• y − √169 = 0 ⇒ y = √169 = 13.

Concept / Approach: Direct evaluation suffices.

Step-by-Step Solution:

Verification / Alternative check: 12 vs 13 confirms the inequality.

Why Other Options Are Wrong: They contradict the established ordering.

Common Pitfalls: Mis-evaluating √169 as something other than 13 or forgetting the “greater root” constraint for x.

Final Answer: If x < y