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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

- \(A\lt(-1)\)
- \(A\geq2\)
- \(A\gt2\)
- none of these

Logic

Inequations

Algebra

But try the problem first...

Answer: \(A\geq2\)

Source

Suggested Reading

B.Stat Objective Problem (TOMATO) - Problem 61

Challenges and Thrills of Pre-College Mathematics by University Press

First hint

\(x(A-x) \lt Ay-y^{2}\) then \(y^{2} - x^{2} \lt A(y-x)\) then \((y+x) \lt A\)

Second Hint

\(|x+y| \lt |x| + |y| \lt 1+1=2\) then \((x+y) \lt 2\)

Final Step

both equations hold for \( A \geq 2\).

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