Question:
Suppose for any real number \( x \), \( [x] \) denotes the greatest integer less than or equal to \( x \). Let \( L(x, y) = [x] + [y] \) and \( R(x, y) = [2x] + [2y] \). Then is it impossible to find any two positive real numbers \( x \) and \( y \) for which:
Suppose for any real number \( x \), \( [x] \) denotes the greatest integer less than or equal to \( x \). Let \( L(x, y) = [x] + [y] \) and \( R(x, y) = [2x] + [2y] \). Then is it impossible to find any two positive real numbers \( x \) and \( y \) for which:
Show Hint
When dealing with greatest integer functions, check the behavior for simple values of \( x \) and \( y \) to explore all conditions.
Updated On: Aug 4, 2025
- \( L(x, y) = R(x, y) \)
- \( L(x, y) \neq R(x, y) \)
- \( L(x, y)<R(x, y) \)
- \( L(x, y)>R(x, y) \)
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The Correct Option is D
Solution and Explanation
By evaluating various values of \( x \) and \( y \), we find that it is impossible to have \( L(x, y)>R(x, y) \), which makes the Correct Answer (4).
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