Let x be the greater real root of x^2 − 365 = 364 and y satisfy y − √324 = √81. 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 exact numerical values derived from simple square roots. The equations are arranged to yield integers after evaluation, simplifying the comparison.
Given Data / Assumptions:
- x^2 − 365 = 364 ⇒ x^2 = 729 ⇒ roots ±27; greater x = 27.
- y − √324 = √81 ⇒ y − 18 = 9 ⇒ y = 27.
Concept / Approach: Evaluate each side carefully. √324 = 18 and √81 = 9. Then solve the simple linear relation for y and compare with x.
Step-by-Step Solution:
x = 27.y = 27.Therefore x = y, which implies x ≥ y (and also x ≤ y).Verification / Alternative check: Substitutions confirm both equations are satisfied by 27.
Why Other Options Are Wrong: Strict inequalities do not hold since equality is exact.
Common Pitfalls: Misreading the radicals or arithmetic around subtracting and adding 18 and 9.
Final Answer: If x ≥ y