Let x satisfy x − √121 = 0 and y be the greater real root of y^2 − 121 = 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: We compare specific solutions: x is uniquely determined by a linear radical equation; y comes from a quadratic with two symmetric roots. By convention, we take the greater real root for y to avoid ambiguity and then compare numerically.
Given Data / Assumptions:
- x − √121 = 0 ⇒ x = √121 = 11.
- y^2 − 121 = 0 ⇒ y = ±11, take greater y = 11.
Concept / Approach: Evaluate both exactly, then choose the correct relation symbol.
Step-by-Step Solution:
x = 11.y (greater root) = 11.Thus x = y, which satisfies x ≥ y (and also x ≤ y). The offered relation set includes ≥.Verification / Alternative check: Direct substitution confirms equality.
Why Other Options Are Wrong: Strict inequalities (x > y or x < y) are false because the values are equal.
Common Pitfalls: Forgetting to select the greater root for y or mis-evaluating √121.
Final Answer: If x ≥ y