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AIME 2025 I / The set of points in 3-dimensional coordinate space that lie in the plane…
Problem
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question
The set of points in 3-dimensional coordinate space that lie in the plane whose coordinates satisfy the inequalities forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form , where and are positive integers and is not divisible by the square of any prime. Find .
Plain-text mathematical notation (without MathML)
The set of points in 3-dimensional coordinate space that lie in the plane x+y+z=75 whose coordinates satisfy the inequalities x−yz<y−zx<z−xy forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form a√(b), where a and b are positive integers and b is not divisible by the square of any prime. Find a+b.
Original LaTeX notation
The set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz<y-zx<z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.Discussion
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