Try this problem from I.S.I. B.Stat TOMATO Objective Problem based on Inequations and conditions.
When \(x(A-x) \lt y(A-y)\) for all x,y with\(0 \lt x \lt y \lt1\), find the condition that holds
Logic
Inequations
Algebra
Answer: \(A\geq2\)
B.Stat Objective Problem (TOMATO) - Problem 61
Challenges and Thrills of Pre-College Mathematics by University Press
\(x(A-x) \lt Ay-y^{2}\) then \(y^{2} - x^{2} \lt A(y-x)\) then \((y+x) \lt A\)
\(|x+y| \lt |x| + |y| \lt 1+1=2\) then \((x+y) \lt 2\)
both equations hold for \( A \geq 2\).
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