Let x be the greater real root of x^2 − 16 = 0 and y be the greater real root of y^2 − 9y + 20 = 0. Compare x and y.

Introduction / Context: Two quadratics with easily factorable forms allow immediate determination of greater roots. We then compare those values directly.

Given Data / Assumptions:

• x^2 − 16 = 0 ⇒ roots ±4, greater x = 4.
• y^2 − 9y + 20 = 0 ⇒ (y − 4)(y − 5) = 0 ⇒ roots 4 and 5, greater y = 5.

Concept / Approach: Factorization and identification of the larger root for each equation.

Step-by-Step Solution:

Verification / Alternative check: Numeric comparison is straightforward; no alternative method needed.

Why Other Options Are Wrong: They contradict the ordering 4 < 5.

Common Pitfalls: Accidentally picking the smaller root 4 for y instead of 5; the prompt specifies the greater root.

Final Answer: if x < y