Let x be the greater real root of x^2 − 32 = 112 and y satisfy y − √169 = 0. Compare x and y.
Aptitude
Quadratic Equation
Difficulty: Easy
Choose an option
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AIf x > y
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BIf x ≥ y
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CIf x < y
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DIf x ≤ y
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EIf x = y
Answer
Correct Answer: If x < y
Explanation
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:
x = 12 (greater root).y = 13.Hence x < y.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